There are hundreds of add-ons out there, and as your journey progresses through the game you will find new ones you like. This is just, as Baloo from The Jungle Book would say, the simple
Lightheaded - Since they inflated the experience benefit in the last patch, using Lightheaded to quest brings experience so quickly it will make your head spin. Lightheaded adds quest information from the comments on the Wowhead.com database site to your quest log. All the information you would have to tab-out for is at your fingertips. I heartily recommend using Doublewide in concert with Lightheaded, which will put your quest log in two panes instead of one to make it fit more easily on the screen. It's like peanut butter and chocolate, two great tastes that go great together. If you want to learn more about Lightheaded check out this awesome article (with accompanying awesome screenshot) from our own David Bowers.
Cartographer - You need Cartographer. Cartographer is essentially "the" map add-on as far as I'm concerned, You'll find all the great features of Cartographer on the page I linked, but the most important Cartographer feature to a new player (who uses Lightheaded) is that when you click a set of coordinates in Lightheaded, it will show you a floating arrow on your screen that points the way to your destination. (As a free tip, I will also mention that you can ditch the arrow and clear all waypoints by typing /noway. Yes, I know you can do it with the mouse, but... I'm one of those weird keyboard people.)
Fubar 2.0 - Fubar and Titan Panel are both addons that essentially do the same thing. They are add-ons that have "modules" that plug into them to offer you various information and services, based on your own preference. Personally I like Fubar a little better because I find there are better modules for it, and because it doesn't seem to suck down as many system resources as Titan. You will need the Fubar addon itself, and then you install the modules into it the same way you install other addons, by extracting them into your \Addon folder.
LocationFu - LocationFu is the #1 reason you need Fubar to begin with. Besides displaying your current location and coordinates in the top corner of the screen, it will also answer one of the most frequently asked new player questions for you, "Where should I go to level right now?" When the LocationFu menu drops down (by mousing over it) it gives you information about the current zone, instances in that zone, a list of recommended zones to quest in, and a list of recommended instances and battlegrounds, all based on your level. The best part is that if you don't know where these places are, you can click on them, and it will give you detailed directions from where you're standing. As far as I'm concerned, this functionality should be incorporated into the game. Hey, I can wish, can't I?
AuditorFu - AuditorFu is good as well if you're going to roll more than one character. It is also a Fubar module, and keeps track of your money on all you characters and summarizes your income and expenses. It's very useful when you see that "must have" item in the auction house and you reach into your pockets and realize you're a few coins short. AuditorFu will tell you which of your alternate characters you need to go and shake to find the money you need.
Possessions - I talked about Possessions a long time ago in Add-on Spotlight and I consider it to be an essential if you're going to make more than one character. Possessions keeps track of all your items on all your characters and in all of their banks. If you're an old-time Possessions lover, you may want to upgrade to the newest version! The newest version now supports guild banks as well!
Some day a mob is going to drop an item you won't want and you're going to need an auction addon to get an idea of what it can sell for. As far as auction addons go, you really have two choices. If you want simple and idiotproof, I would go the Wowecon.com route. Wowecon has a bit of an unconventional setup in that it loads before you run World of Warcraft and downloads new auction price data from their site. This information displays in tooltips when you mouseover an item. When you exit the game, it anonymously sends the information it accrued about your auction transactions back to the site to add to their database. For most people, I find this is the simplest and easiest solution. When you find your needs are no longer met by Wowecon (or you just don't like it) try Auctioneer. It's easier to install, but a little more complicated and time-consuming in it's operation. Auctioneer is probably used by a lot more people, so finding a friend to help you won't be a problem.
The best way to find out about new and just otherwise great addons (besides reading our Add-On Spotight column regularly) is to find a guild that has smart knowledgeable people in it, and just hang around them. Ask on the guild forums what people use. The great thing about addons is that if you download one you don't like, all you have to do is delete the folder and it's gone.