There are a number of sites to find addons, such as WoW Ace and WoW Interface, but my favorite is Curse due to its screenshots, overview, categories, search function, and user comments.
I am currently using:
Cartographer: One of the best map addons you can get. It'll store and display the locations of vendors, trainers, and quests on the minimap, you can set waypoints, and a whole mess of other features.
MetaHud: This will display your health and mana as curved bars near your character so you don't have to keep eyeballing the upper left corner. Your target's health and mana are displayed next to your own, so it's easy to compare how you're doing.
MobInfo2: Awesome mod that actively calculates an enemy's actual health by the damage you do to it, then displays the result. Also keeps tabs on what that mob drops and the frequency of those drops, among other handy features.
InFlight: Tells you how long a flight will take and creates a nice little time bar during flights so you know how long you have to go pee or cook dinner. =oD
GrimoireKeeper: For Warlocks, it makes Demon tomes simpler by color-coding them according to whether your pet already knows the ability or if they can learn it.
That's all I'm using at the moment, though considering grabbing Fubar or Titan Panel. Auctioneer is also a fantastic mod if you use the Auction House. So, what do you use?