So, a blog much more widely-read than this one recently posted about doing away with XP tables and transitioning to achievement-based advancement. This reminded me, naturally, of Samhaine's series "To End an Era of Exp," particularly the concluding post. Notably, Samhaine was really talking about video games, but the ideas there might be applicable to tabletop as well.
I was thinking about what's really going on here, and it seems to me that this is pretty much the same as using 4e's quest-goal rules as the only source of experience points. Telecanter's idea, then, is a quest-only system with meta-game quests. (Just to be clear, I use the term meta-game here without prejudice.) A goal like "survive a dicey combat" is a goal about the game side of things, while "defeat the ogre warband" is a specific story application of the same goal. "Outwit a trick/trap" is a game goal; "Only the Penitent Man Shall Pass" is a specific trap to bypass within the progress of the story/dungeon. Neither way is particularly better - my point here is just to show variations on the scheme.
As it looks like Telecanter realized in his following post, an achievement-based system does not play nice with editions of D&D prior to 3rd, in which classes have uneven advancement charts; sorry, OSR guys. It's also less than ideal for systems that aren't based off of character levels, such as the World of Darkness; while you could assign a number of character points to each specific achievement, it's not as interesting a change - XP aren't replaced, just bundled.
Anyway. Thinking along these lines, a GM could use these meta-goals to encourage any number of different things. The first that comes to mind for me is stunt usage: page 42 of the 4e DMG has rules that offer scaling DCs and damage values for stunts, but from what I can tell the vast majority of gaming groups don't think to use them this way. Thus a GM might offer an XP bonus of (25 xp * current level) to all party members each time a player comes up with a new and unique stunt. If this seems too generous, offering that bonus a limited number of times per session or per level would be reasonable.
In the comments following Telecanter's post, more purely in-world achievements were discussed, which brought to mind for me the circle tests used in our LARP magic systems. SI was the first game I know of to include a circle test mechanic, and from the beginning we've faced the same problem in its implementation: players need the specific intervention of an encounter in order to continue their advancement, and they grow understandably frustrated when many events pass before their circle test encounter finally shows up. On the other hand, these encounters can be some of the most personal and intense scenes in the game, since SI's sorcery and all of KG's schools of magic tailored those encounters to the character. The problem with something like this in the proposed achievement-based advancement system, of course, is that not only can the player not advance within his form of magic, he can't advance in any other way either. At least in CI/RBP games, you can just spend your XP on something else, or save them for a future large purchase.
There are a lot of fiddly details at stake here, each with their own benefits and drawbacks. I won't try to go into each possible iteration, because I'd like this post to remain at least marginally readable and less than a hundred pages long. The one that I think is important is offering slightly more goals than the number required to advance. Much like earning merit badges in Scouting, players will probably always see some of the achievements as the lowest-hanging fruit. Certainly this is how I've seen players approach plot goals in the past, when they've tabulated everything they want to accomplish.
Outside of replacing experience-based advancement, it would be cool to have in-play organizations that reward specific accomplishments: the Fighter's Guild or your Warrior Order rewards you for vanquishing a superior foe, demonstrating mastery of a particular strike, and forging your own weapon. The Ancient and Accepted Order of Ruby Magi promotes you when you (pick three): rediscover a lost spell (or create a new one), defeat a frostwraith (the Order's stated purpose), donate a completed magic item of at least a certain value, and undertake the Third Trial of the Burning Gem. This folds back into the organization advancement systems presented in the 3.5e DMG2; what I find particularly interesting about this is that you could write these goals in an in-character way and thus make them completely a part of the roleplay. I guess that's my only real problem with meta-game achievement-based advancement: if the goals aren't things that the players can't help but complete in the course of play, the characters will need to seek those things out, and may lack solid in-character motivations. Much as I hate to hear in-character references to experience points, I would hate to hear "we need to find someone or something to outwit... that's really our main goal at this point."
Anyway, below the cut: Sample Achievements. Ten per level, pick... let's say eight.
1. Defeat an enemy of at least 4 HD/4th level/CR 4.
2. Defeat a group of at least 6 enemies of 1 HD/1st level/CR 1.
3. Bypass or survive a trap of at least 4th level/CR 4.
4. Reach the second level of a dungeon (for OSR dungeoncrawlers), or spend four weeks in the wilderness (for hexcrawlers). (Honestly, just having an achievement for the passage of in-play time does some interesting things to the game, encouraging players to let time pass.)
5. Return one of the captured villagers safely home (implied: Escort quest).
6. Establish a recurring patron NPC.
7. Gain a permanent magic item worth at least 1,000 gold (3e value numbers - for 4e, an item of level 3 or higher), or consumable magic items worth at least 2,000 gold (4e: ...um, you know, whatever).
8. Survive in a bar brawl with at least 10 other combatants.
9. Talk your way out of a fight with Hostile opponent.
10. Find the entrance to the Temple of the Hidden King.
1. Defeat an enemy of at least 5 HD/5th level/CR 5.
2. Defeat a group of at least 6 enemies of 2 HD/2nd level/CR 2.
3. Bypass or survive a trap of at least 5th level/CR 5.
4. Reach the third level of a dungeon, or spend four weeks in a more dangerous wilderness.
5. Return one of the treasures stolen from the Academy.
6. Learn a secret about your recurring patron NPC.
7. Gain a permanent magic item worth at least 2,000 gold (4e: an item of level 4 or higher), or consumable magic items worth at least 3,000 gold.
8. Win a contest of skill during a village festival (horse race, archery, footrace, wrestling...)
9. Intimidate an opponent of at least 4 HD/4th level/CR 4.
10. Enter the Second Fane of the Temple of the Hidden King.
1. Defeat an enemy of at least 6 HD/6th level/CR 6.
2. Defeat a group of at least 7 enemies of 3 HD/3rd level/CR 3. (Since AoE effects are a bit more feasible for party wizards at this level in most editions...)
3. Bypass or survive a trap of at least 6th level/CR 6.
4. Reach the fourth level of a dungeon, or something something wilderness.
5. Rediscover a long-lost spell (arcane or divine) or alchemical formula, or develop a new spell or alchemical formula.
6. Cultivate a relationship with your patron's direct superior.
7. Gain a permanent magic item worth at least 4,000 gold (this is damn hard at 3rd level in 3.x; 4e: 6th level or higher), or spend at least 1,000 gold creating magic items.
8. Convince an enemy to become a loyal ally.
9. Succeed a dangerous non-combat challenge requiring at least eight difficult skill checks.
10. Discover the connection between the Temple of the Hidden King and the dark forces threatening the village.
Available at any level:
1. Develop a stunt into a signature move. This probably requires design work on the part of the player and the DM.