Various news outlets (I heard chez Relmstein) are reporting on a recent interview in which Blizzard claims that WoW achievements are the first step in what is going to become a Blizzard Level, a Gamerscore like number that will carry forth to Diablo, Starcraft, and hypothetically any future Blizzard games (if they ever make any new IP's). As such, those of us who care about meaningless numbers that record what we've done in the game have no time to waste in getting to work on those achievements today.
What's that, you say, Achievements are a feature of the yet to be released expansion? Not entirely. You won't get CREDIT for said achievements until the expansion (or at least patch 3.0) launches, but that doesn't mean you can't start working now if you're so inclined. In fact, the UI records the date on which you completed the achievement, so you'll be rewarded with an earlier completion date (whenever the patch goes live) than players who don't start until the system is launched. Here's a guide to what you can and cannot do in the present.
Can Do: General Character Stuff
If you're not level 70, head for the cap. There's an award for having purchased all seven bank slots, and equipping a ["Gigantique" Bag]. Examine your local database for more such candiates.
Can Do: Quests
There are achievements for total quests completed, quests completed in each zone of Outland, and for completion of all the quests from Nestwaringway's two camps.
CANNOT DO: Daily Quests
Repeatable quests (such as dailies) do NOT count for total quest achievements, and achievements related to daily quests are not tracked in the current TBC client.
Can Do: Profession Achievements
There are profession achievements for each tier of profession training. If you've got both of your tradeskills maxed, you can get the achievement for double grand master immediately, along with capped First Aid, Cooking, and Fishing (but see below).
Partial Effort Wasted: Fishing
In principle, you can cap out on fishing now and go fish in Northrend as soon as you'd like. However, there are a number of fishing-related achievements in the expansion that involved fishing in various locations around the old world, all of which are good for skill points (you are equally likely to get a fishing skill point anywhere in the world, regardless of minimum casting skill level, as long as you can actually catch the local fish). It might be better to wait until you can get BOTH achievements AND fishing skill from the same effort, especially if you're not fond of fishing.
Can Do: Non-Raid Reputations
Most reputations that can reach exalted status are worth achievements. (AFAIK, the Steamwheedle Cartel is currently not worth anything because getting them to exalted really isn't intended.) Some of the more onerous (notably the Alliance Wintersaber trainers) are not. The major exception is raid zone factions. If you can get rep outside of a raid, it's probably still good (e.g. Argent Dawn, Cenarion Circle), but if you can't (Violet Eye, Hydraxis, Zandalar), it's a zero-point "feat of strength" instead of an achievement for you.
Partial Effort Wasted: PVP
You can work on your total honorable kills and your battleground (AV/WSG/AB) reputations now for more achievements. However, there are many many achievements related to PVP that you will get just for being in the battleground. I would NOT advise doing PVP solely for the achievement work at this time (though it's fine if you want gear, competition, etc).
Can Do: Exploration
There are achievements for fully uncovering the map in every zone in the game. The good news is that, when the system goes live, you will have a checklist that tells you which spots in any given zone you've missed. (I was only missing a single spot in Outland thanks to flying around for dailies.) However, that doesn't mean you can't work on this now. One thing I found helpful was the use of Cartographer, an Ace mod that includes a function called "Foglight". By default, Foglight uncovers the entire map of each zone so you can see where you're going. However, Foglight can be configured to light up each unexplored portion of the map a prominent color of your choice. You might miss a spot or two, but I found that this feature generally worked well in helping me fill in the gaps on my mage.
NOT RECOMMENDED: Exploring Teldrassil as a Horde
This bullet point speaks for itself. The Alliance has a few inconvenient spots to get to (for instance, it is easy to accidentally wander into Thunder Bluff, flagging yourself for PVP), both factions need to avoid level 65 guards outside enemy newbie (level 1-5) subzones, and the Horde does need an Alliance-guarded boat to get to the Draenei starting area. However, nothing compares to the inconvenience of riding through Darnassus (which requires you to zone into the city via a teleport that can lag slow computers, and is the only corpse run I know of in the game where you must ride a boat as a ghost to return to your body). I would NOT recommend this to Horde characters before the expansion, simply because it would be very annoying to have to repeat the trip upon discovering that you missed a spot.
CANNOT DO: Kill Achievements
If it's a raid or dungeon "kill X boss" achievement, it appears that you will NOT get credit for it retroactively.
Can Do: Collections
Mount, minipet, and tabard collectors are all awarded with achievements. I would NOT recommend purchasing mounts and minipets from a vendor until the expansion simply because they will take up bagspace now and won't if you wait. That said, if you've always wanted a bit more variety, you can rest easy knowing that you will get the extra bagspaces back in a few months.
General Rule of Thumb: Non-repeatable ftw
In conclusion, generally you're looking for things that cannot be repeated (e.g. if you're already exalted, you can't get exalted again), or for things which can concretely be proven (e.g. own X items). If it's something that that is repeatable, and you do NOT want to do it, it might be better to wait until the achievement system goes live so that you know you'll get credit.