A discussion in the comments of my previous post brought up the many different forms that multi-classing has taken over the years in D&D, so I thought I might explore that in a post. It's also something that Kainenchen and I have talked about many times, because there are a lot of nuanced difficulties in every system that has yet been advanced. I'll start by saying that no edition has presented a perfect system, but their flaws have been wildly different from one another. As usual, I'm starting with the earliest edition that I ever played. Oh, and fair warning - this might get super-crunchy, but that's partially a result from multi-classing always involving more complex bookkeeping than single-class characters.
AD&D Second Edition
2e has two very different multiclassing systems, "multi-classing" and "dual-classing." Of these, multi-classing has the most in common with 4e's hybrid-class system, while dual-classing... has little in common with anything that has been done since, for reasons that will become obvious. Multi-classing lets demi-human characters (only) have two character classes, dividing your XP equally between them and only gaining half value of each hit die rolled (effectively granting the average of the hit dice of your two classes). Because of 2e's idiosyncratic advancement charts, such characters generally have uneven levels in their two classes, and are generally 1-2 levels (but not much more than that) in each class behind single-classed characters with the same overall XP total. This is a pretty clear outgrowth of the OD&D Elf class. Certainly elf fighter/magic-user is one of the best multi-class combinations in the game, since they get the additional benefit of being able to wear elven chainmail and still cast spells. Characters can even add a third class to that mix; elves can add thief progression, and half-elves can add thief or cleric progression (if I recall correctly). There are very specific lists of the classes that can be combined, based on race, and you can never combine two classes of the same header (that is, no fighter/paladin or bard/thief). The whole system is some of the most intensive bookkeeping that you'll find in 2e, which is to say that it is a bit of a pain, but still doesn't hold a candle to the bookkeeping of later editions.
Dual-classing, on the other hand, is restricted to humans, and involves starting the campaign single-classed, progressing for awhile, and then dumping every part of that old class except for the hit points while you gain experience in a new class. For all intents and purposes except for hit points, you are a first-level member of that new class, though presumably with a bit of accumulated treasure. Once your levels in your new class equal your levels in your old class, however, you regain all class features of that previous class, and can start gaining hit points from hit dice again. I don't know what to tell you. I absolutely never had a player hint, even jokingly, that he was considering dual-classing, because once the rest of the party is having adventures appropriate to 6th-level characters, do you really want to go back to having the abilities of a first-level character?
The good side of the multi-class system is that it's surprisingly close to balanced. It turns out that having two classes at about two levels lower costs you just enough that your single-classed companions aren't too badly overshadowed. The hit points that you're missing do sting a bit, but the overall gameplay environment of 2e and prior editions was much less focused on the tank/DPS/heals dynamic of later decades. The fact that you're contributing slightly less to the party's overall effectiveness just doesn't matter as much in 2e as it does in 4e. The bad side of the multi-class system is that you can't just dabble - if you want to be 80% fighter and 20% magic-user, that's not really an option, since you must divide your XP equally. The system is necessary in the first place because of 2e's atrocious demi-human level-capping rules, for which I have only fulmination. Anything that lets you gain more overall power and continue to gain XP at the "normal" rate a little longer is a good thing. There is no good side to the dual-classing system as far as I am aware.
The one thing I don't know, or have totally forgotten, about this system is how DMs are intended to award experience if, say, a fighter/magic-user spends the whole adventure behaving as a magic-user and totally ignores his fighter side, assuming the campaign is using XP awards for "class-appropriate" behavior.
The problem shared by both of these systems is that they explicitly contradict the world-logic that TSR put in place to justify level-capping demi-humans and not level-capping humans. To wit, demi-humans lack the focus necessary to stick with one class. Doesn't dual-classing represent a lack of career focus much more clearly than multi-classing? If anything, you'd have to call multi-classing the superlative ability to focus on two or more things at once, while dual-classing is getting bored and moving on to something else. In the best available real-world terms, which one is more flighty: the person who earns two simultaneous doctorates (actually, I might believe this as a representation of "elves don't sleep") or the person who gets an associate's degree in journalism, goes to med school for seven semesters, and then moves on to some third unrelated thing? (Okay, humans can actually do the latter and be awesome, because experience is additive - the point here is that they might legitimately be considered flighty.)
Oh, and there was something that could be called a gestalt system, if you squinted a bit; there were optional rules in the DMG for building custom classes, with the class's features, restrictions, and so on determining its XP chart. I certainly wasn't about to let players even discuss custom-building classes, no sir. Good lord, no. Skills and Powers also did some nominally roll-your-own stuff with classes, but it mostly stayed within a single archetype.
Anyway, let's move on to more logical but equally problematic approaches.
D&D Third Edition
In more ways than I can name, 3e reacts against the illogic of 2e with systems that are intensive on bookkeeping and adhere to simulationist logic, leading to things that look very strange from a more gamist perspective. Though later releases introduced several alternate approaches to multi-classing (on which more later), the first version of multi-classing was strictly additive, based on the new unified XP chart. The unified XP chart tracks character level rather than class level; you just decide which classes you're going to spend those character levels into. This makes sense if you think of gaining a level in a single class as spending time in training for that one thing, but less so if you think of your character's multiple classes as a mechanical representation of overall power. There are also experience point penalties for having classes of uneven levels, unless your race allows you to ignore one of those classes because it has "favored" status for you. This is to stop you from building a dwarf wizard 5/cleric 2/rogue 2 or whatever other unholy combination you might gain. There certainly are classes in which "splashing" one to four levels of the class grants a disproportionate amount of the class's appealing features, so this is potentially a useful control, but it adds a lot of mental overhead to multi-classing that almost never matters.
The real problem with 3e multi-classing is that high levels of any class grant more power than low levels of any class. Just to break that down a little more: okay, yes, going from Ftr 1 to Ftr 2 does roughly double that character's effectiveness, but going from Ftr9 to Ftr 9/Wiz 1 is much less powerful (since you'll need to completely rethink your gear, etc.) than going to Ftr 10. This same problem becomes much more significant with spellcasting classes, because a monster's saving throw values and spell resistance, if any, have scaled up; only high-level spells have much chance against the former, and only high caster levels have much chance against the latter. You can get pretty close to this mathematically by thinking of actual power as an exponential function (hint: don't take this too literally):
Overall power = a2 + b2 + c2..., then Ftr 9 = 81, Ftr 10 = 100, and Ftr 9/Wiz 1 = 82. Ftr 10/Wiz 10 definitely can be as closer in power to an Ftr 20 than this would indicate, but it's probably still weaker overall unless you really know what you're doing.
This all ignores the fact that you also need to have at least two very good ability scores to pull off this kind of multi-classing. 3.5 did eventually introduce feats to even things out a bit, but you're still paying more potential power playing catch-up. The one place where this system works pretty well was with class combinations that involved no emphasis on spellcasting at all; of these, fighter/rogue is probably the best all-around, as there are good gear solutions, the rogue's skill points shore up one of the fighter's key weaknesses, and the class abilities otherwise complement each other pretty cleanly. The huge problem with fighter/rogues is that the order you take these class levels in matters very deeply, so there is a considerable amount of bookkeeping nightmare at stake; also, characters starting after first level either have a big advantage or a hell of a headache. (If I wanted to extend the mathematical metaphor to make sense of why fighter/rogue multi-classing works, I'd point this out, but because friends don't link friends to TVTropes, I won't.)
Which brings me to some of the game's more... daring... approaches to multi-classing. Let's start with the prestigeclasssolution. Since the release of 3.5, there have been bitter disputes over the balance all of the multi-class prestige classes, but especially the arcane trickster and the mystic theurge. I suspect that the Fochluchan lyrist and the various Daggerspell classes are awful too, but I don't really know. To focus on just one, I'll go with the mystic theurge: the class casts both cleric and wizard spells as if it were a character of three levels lower. In real terms, that means the character's best spells are a level and a half behind a single-classed character. The throughput is basically identical to a 2e cleric/magic-user, except that someone might realistically play 3.x up to the mid-teens; anecdotal evidence indicates that this was vanishingly rare in 2e, and racial level limits would have theoretically stopped or slowed this anyway. From what I understand, the mystic theurge only really becomes a problem toward the end of the class's progression. What the hell, let's see what the math says.
Wiz 3/Clr 3/Mystic Theurge 10 ≈ Wiz 13 + Clr 13 (missing a _very_ few class features, but closer to correct than any other numerical choice would be). 132 + 132 = 338. 162 = 256. So if you're inclined to accept my highly-spurious math, the Mystic Theurge's superiority is obvious!
The first-party and third-party glut of 3.x publishing ensured that there are countless other multi-classing systems, including the gestalt system (which is more a variant campaign style than an actual multi-classing system), a level-substitution system (in 3.x, this is chiefly for racial levels; in AE this is just a character-customization thing), and probably a few other variations that I'm overlooking. Oh, and d20 Modern deserves an honorable mention: the basic classes are sufficiently unified in their mechanics yet limited in their progression that the game expects a high degree of multi-classing between them as a means to get into advanced classes. The takeaway here is that people tried other stuff, none of which exactly caught on in the broader community.
D&D Fourth Edition
4e completely changed the fundamentals of what characters get from classes and when they get those things. Passive abilities and class features come from the first level of a class, paragon path, or epic destiny, or from feats. The three different systems of multi-classing in the game boil down to whether you want to sacrifice:
Feats - this is the dabbler's option. Very easy on the bookkeeping.
Paragon Path - this is for people who can wait until 11th level to actually become multi-classed. Not much worse on bookkeeping than a paragon path.
About half your class features and about half your powers - this really kind of turns your two classes into one class. Not for the faint of heart!
The problem underlying all 4e multi-classing is that powers gained from multi-classing don't change the ability score that governs the attack and damage modifiers. Since there is no build of fighter that benefits from Intelligence, there's really no chance of seeing a fighter/wizard multi-class. Much like the way that ability scores give players the impression that some classes simply cannot go with some races, classes that don't at least partially share stats can't really go together. (For my own solutions to this problem, see here.) Weapon/implement mixed usage is also an issue for some potential multi-class options. Fortunately, WotC published the swordmage and the hexblade warlock to take the place of more tanky and more DPS-y fighter/mage builds, respectively.
The good thing about 4e's system is that a player can choose her own level of involvement in Project Multi-Class. If you want a slightly toned down version of one class feature from another class, you can have it. (Balance is sometimes dubious, particularly when picking up class features that grant healing.) Spending further feats lets you trade out more of your original class's powers. This does mean that the synergy with your core class needs to be awfully strong (or it has to really make your character concept sing), since you're paying a significant amount of power for the privilege of a (nominally) 1-to-1 exchange.
Over the course of these three rule setsand many internal subsystems, everything kind of comes down to two fundamentally different approaches to multi-classing, arguably derived from two different views of what a class is and what rules mean. In the one version, seen particularly in 2e and 4e, multi-classing is creating a 50/50 or 33/33/33 blend of your classes. It's essentially a new class that you live in; the component classes are the available blocks of rules-code that you graft together. Rules are a way of expressing and talking about the world, and sometimes you have to squint a little... or a lot... to get the rules to describe that world (much like dealing with clunky-but-tolerable code).
The other version, seen in 3.x but exemplified by Earthdawn, is multi-classing as a conscious, in-character choice to train in another path of study or power for a little while. There's much more of a sense that classes have objective reality in the world, and can be discussed in-character in that light. To dabble in the fighter class is to say, "I want to be better at melee combat (but not in a rogue-y way)." In a sense, these classes are something more like an extremely low-granularity point-based system. It's certainly not the only available interpretation of 3.x rules, but I think a significant portion of its playerbase would agree the rules can be understood as the world physics. The rules aren't there to help you describe and resolve a separate world.
The 3.x approach also works well if you wanted to purge all but the core four classes (OSR arguments aside, dropping the rogue would be a serious mistake here); 3.5's Unearthed Arcana offered something very similar to this with the warrior, adept, and expert classes. Want to play a paladin? Try fighter + cleric. Maybe your 20-level progression is Ftr 5/Clr 15, Ftr 16/Clr 4... it really doesn't matter. Just... make sure you strip as much setting flavor as possible from the classes, or these building blocks will have a lot of undesired cruft that clutters up the constructed character.
I hope that D&D Next will find a way to embrace both of these views, since they're making all of their rules modular anyway. ENWorld has reported from the class design seminar that they're planning on using 3.x-style multi-classing, but the details of class design could avoid the problems that result in that system. If they're going to embrace fans of every edition and be as universal as they hope, it's all but compulsory to offer two or more subsystems: one to make classes the rules code with which you build that ideal character in your head, and one to make classes the character's decision of what to learn next. There are quite significant balance problems to solve in either case - and don't make the bookkeeping too much of a pain - and... good luck with that. One thing that 5e seems to have in its favor so far is that caster level is not an all-important stat to determine a spell's duration, damage output, and ability to defeat spell resistance. The next thing they need is some kind of rule allowing-with-drawbacks the casting of arcane spells while wearing armor, or arcane armor that is at least close to the defensive power of the armor that the multi-class wizard's other class says he should be wearing.
The other thing that 5e has going for it is the multiple levers of class, background, and theme. These seem to support the dabbler quite well - we've seen one concept of a "cleric who fights" with the guardian theme, and the ever-popular fighter/mage or rogue/mage concepts look like they'd be supported pretty handily with the fighter or rogue class (respectively) picking up the wizard's Magic-User theme. It remains to be seen, of course, how much players will feel like they have to sacrifice in order to take a theme that is slightly outside of their class's core concepts. It also sounds like characters will add on further themes at higher levels, sort o like paragon paths or prestige classes, but possibly redirecting the character's overall feel to a lesser degree.
I guess that means, ultimately, that they might have both 3.x multi-classing and (to coin a phrase) multi-theming. It's practically a koan - when is multi-classing not multi-classing? When it's all about finding ways to describe and refine your character's High Concept Aspect.