Not that long ago in G+, Rob Donoghue proposed the idea of distributing secrets to players at the start of play by means of a card draft. Shortly before Cam Banks posted the same idea, it occurred to me that starting character stats could be distributed with a card draft too. Now, Cam Banks is at least a thousand times more famous than I am, but I'm still going to take my own run at the idea. By no means is this approach right for every game, so I'm also going to talk about the kinds of games where it could fit well.
The strength of the idea is that character creation should wind up a lot more organic than a completely planned system, while at the same time including elements of choice. The weakness of the idea is that players who only want to play one race, class, or background, or players dedicated to optimization, may not get what they want. There's also a pretty reasonable chance that two characters in the same group won't be balanced against one another. I haven't tested the idea yet, by any stretch of the imagination.
Start with a deck of cards with a variety of different abilities or bonuses written on them. Personally, I like the idea of cards involving two choices; in a D&D context, this might be "+1d4 to one ability score, or begin play with a treasure map to a destination within a day's journey." Now, it's probably the case that a lot of players choose the numerical bonus over the story option, but that's not the worst thing in the world.
A deck suitable to a group includes enough cards to give them stats, and to make sure each player has several choice points. For D&D, this might mean a final hand of 10-12 cards per player, of which they use all but one or two to determine the character's abilities. For WaRP, this might mean a final hand of eight cards, of which 4-6 determine the character's abilities. As in a draft for a card game, you generally want to leave in some room for discarding cards you simply got stuck with, and never especially wanted.
The drafting mechanic itself is nothing new. I recommend splitting the (shuffled) deck into a number of piles equal to the number of players; each player selects one card and passes to the left. A snake-draft style is fine, but slow, since every player has the whole deck to consider.
I strongly encourage a strict ban on table talk during the draft. The whole point of the idea collapses if players discuss and collaborate in the process. Also, with this many choice points and ways for players to influence other characters, many groups would find that one or two players "quarterbacked" the experience, rather than allowing the characters to form organically. Guidance from a more experienced player is usually helpful to making sure newer players have a good time; I'd simply say that drafting has enough choice points that it may not be appropriate for groups whose players have widely differing amounts of experience with the game.
One of the weird things about drafted character creation is that it seems to present adversarial character generation. If Alice takes a card, necessarily Bob can't have it, right? That tone suits some games (Amber, Lords of Gossamer and Shadow) but not others. To water down the adversarial stance, many cards have an effect on the player to the right of the one who selects a card. This means players can't help but do nice things for one another, even if it isn't the benefit you would have chosen for yourself. These peripheral abilities always apply - the player who drafts the card doesn't have to choose that ability from the card.
Another wrinkle I added to the system is Drawback cards. Drawbacks encourage players to spend some of their precious draft selections where they otherwise might not, because Drawbacks only kick in when the players have used all of their draft selections and handed the remaining cards back to the GM. Drawbacks are plot-level Bad Stuff, usually not directly changing a character's stats. Using Rob Donoghue's ideas as a springboard, I felt like having the draft influence the early plot of the game would be interesting.
Some cards present quests instead of direct adjustments to ability scores. As with Drawbacks, I wanted the draft to influence the story of the game. In these particular cases, the quests provide sizable bonuses to ability scores, generally better or more reliable than what you can get from non-Quest cards.
General Rules for Drafting
No table talk until the draft is complete. All players keep their drafted cards secret until the end of the draft.
Create a separate, randomized deck for each player (not including the GM), with a number of cards appropriate to the system.
For the D&D Next deck linked above, this is 12 cards per deck. (I've currently created a 52-card deck; in the longer term I'd want to create more cards, so as to support parties larger than four.)
After drafting a card from a deck, pass it to your left.
Continue the draft until each deck has only two cards remaining. Return the remaining cards to the GM.
Order of Operations:
For any cards with a Resolve This First ability, choose which ability you will apply.
Abilities with Resolve This First are applied immediately, when chosen.
All adjustments from "Player to your right" resolve next.
Players resolve the rest of their cards in any order they like, rolling any indicated dice at the time the card is resolved. When a card specifies "increase" rather than "set," the adjustment applies only if it is higher than the pre-existing score.
Other than Resolve This First cards, choices between a card's abilities are not binding until that card is resolved.
Most systems require players to have certain non-numerical attributes that are also derived from the cards. If a player ends the draft without at least one card granting the necessary attributes, the player may offer cards to other players as blind trades, in exchange for attribute cards, specifying only the category of the attribute they need.
In D&D Next, for example, each player must have a class, race, and background.
D&D Next Rules for Drafting
In addition to the rules noted above:
All characters start with a base of 8 in every ability score, and build from there.
This system is best suited to starting characters at third level. Characters wishing to multiclass must draft each of their starting classes separately, but they choose the split of their three levels between those classes. Characters do not have to follow the normal rules for ability score prerequisites to multiclass at this step.
Upon leveling, characters can multiclass into other classes according to the normal rules.
Ability score adjustments from cards cannot increase above 18 or fall below 3. If an ability increase would push an ability score above 18, the score becomes 18 and the excess value is lost. Ability score adjustments from race, class, and leveling ignore this rule.
Characters cannot have more than one race or background, as usual for D&D.
If a character needs to come into the game late (perhaps due to the untimely demise of their previous character), the primary drafting model obviously won't work. Fortunately, I play Hearthstone just like everyone else, so I've seen how solo drafting can work. The GM builds a single deck of as many cards as all of the original draft decks combined, making sure to include several cards for each necessary attribute. Deal a number to the player equal to the party size; the player chooses one card and discards the rest. Repeat until the player has the normal number of cards to construct a character; if the player winds up without any options for a necessary attribute, it's a misdeal.
When to Use Drafted Character Creation
Short-term games are great for drafted character creation, because the worst available outcome is that you have a character you don't absolutely love for a session or three. Not all of the sample cards are well-suited to that, of course. The GM should cut quests that you cannot possibly complete or drawbacks that cannot possibly come up and replace them with something more applicable. The great thing about short-term games is that adhering to the core rules structure of the game is less important than it might be - so replace those quests with unusual abilities that lie outside the class structure, and let the characters be all the more memorable.
Systems that don't have a lot of required attributes (races, classes, Paths, Bloodlines, whatever), such as WaRP or a mortals-only New World of Darkness, are great for drafted characters, because the issues of lacking a required attribute never emerge. The more wild and off-the-wall a starting character can be, the more interesting this process can get - again, WaRP is a top candidate. I don't know Amber Diceless or Lords of Gossamer and Shadow very well, but I am pretty sure that drafted character creation would be just about perfect for them. Spirit of the Century, Fate Core, and Fate Accelerated should be more or less workable; Dresden Files, rather less so, since each different type of character uses nearly unrelated rules. SIFRP would either be great or unbearable, depending on how often a character got stuck with Fighting 5d and Athletics 1d, or the like; all in all I expect it would be a mess.
Anyway, I make no claims whatsoever that this drafted character creation would be balanced, or equally fun for everyone. But then, rolling for ability scores hasn't delivered that either, so I don't feel too bad about that.
Edited to Add: Systems Sans Setting has expanded upon this idea in some pretty excellent ways. His version is for Pathfinder, but would apply to many other iterations of D&D with minimal modification.