There's a decent list of achievements on MMOC now, possibly more still to be added. So far there are two types.
The counter type doesn't really do anything other than count the number of times you've died, been resurrected, used the /lol emote, flasks you drank, kills in pvp, highest strength, highest armor, etc. Nothing other than just mildly interesting for historical purposes or for showing off.
The second type however, awards you "achievement points". Completing each task will give you a score varying between 5-100 points. The exact purpose of the points (other than tracking the total) isn't clear yet. Perhaps you'll be able to spend the points at a later time to buy some items or a tabard, time will tell.
Character. Exalted with X factions, highest stats, number of items won, potions drunk, gold gained and spent.
Deaths. Total deaths in each battleground, by the hand of certain bosses, and number of times resurrected by each class.
Feats of Strength. Obtained certain legendary or highly prized rare items.
Kills. PvP kills, PvE kills, critters killed.
Social. Number of groups, guilds, times /lol and more.
Statistics. Damage and healing records and totals, flight time, number of quests completed, times summoned.
Achievements + Counter
Player vs. Player. Get 100, 1000, 10.000 kills, arena ratings achieved, killed faction bosses.
Professions. Cap each profession, fish up weird stuff. Total number of items enchanted.
Dungeons & Raids. Defeat each instance boss in the game.
Exploration. Fully explore each zone.
General. Vanity pets, total gold, bank slots obtained.
Quests. Complete X number of quests, slaughter seals.
Reputation. Exalted with X factions.
World Events. Brewfest, Hallow's eve, Lunar festival, Winter and other seasonal events.
Blizzard has stated that anything currently in game will be tracked retroactively. Meaning, total map explored, exalted factions, lifetime honorable kills, total vanity pets, bank slots, legendary items obtained, etc. Stats such as the total times /lol used, number of deaths by boss X, total number of raids, total number of guilds, are not possible to be applied in the same way. You'll be able to start earning these as soon as the 3.0 expansion patch is released.
I wouldn't care too much about the counters myself, the achievements should be fun to collect however. I know there'll be at least one person in our guild that'll for sure go out of his way to destroy 1.000.000 Tuskarr, just to get that achievement. He shall remain unnamed for now. But, I doubt there's a single person in our guild who doesn't know the answer to that... Which does give a new idea for a poll.
How many achievements are you aiming for?
See deatknight.info, WoR or the the official blizzard page (posted 17th july 2008) for related screenshots and info on achievements.