I agree with both Q and Odale. Two years ago, I can't imagine playing without addons. But now ... some formerly really important addons have been built into the game. Questhelper is now built-in. Equipment Manager/ItemRack is now built-in. Floating Combat Text is now built-in.
And in some cases, functionality has overcome the need for addons. For instance, as a Moonkin, Squawk and Awe is somethign I used to watch eclipse cooldowns. But eclipse now works COMPLETELY differently so it's moot.
Some addons stilll help gameplay. DBM. Recount. Grid. Omen/Threat. Quartz. Some remain really convenient info sources or functionality (Fubar+MoneyFu+PerformanceFu+etc ... although Fubar still hasnt' been updated for 4.0.1 so I'm considering moving to Titan ... suggestions anyone?). Vendorizer (sells gray items automatically at vendor). ReputationWatch that switches the reputation on the XP bar to whatever the last thing is that you got rep with. Tiptac (to relocate and reshape the tooltip). Razernaga (barmod I use since I sometimes use that mouse, and it's a decent barmod). Auctioneer.
If I were restarting playing the game, I'd start with as few as possible -- Odale's setup. Then gradually build up with what people recommend and when you say "hmm, I wish there was a mod that did X" and found it.