The User Interface is arguably the most important tool you have as a player.
While the default UI worked for me for the first few months I played, when I first found out that I could make my WoW user interface look however I wanted, I was so excited. That was shortly followed by a lot of frustration, mucking around with different mods and creating a constantly changing style. I know what I like now, but it takes a while to get it right.
Addons used for levelling are pretty different from those used for end-game content, so I have just installed those that I am using during levelling for now, and listed a few of those I find most useful here. I hope you find something useful in this list too! I've added links to curse.com but you can also download them from a variety of other sources such as wowinterface.com.
1. FuBar 3.6
Fubar puts a thin bar across the top and/or bottom of your screen. A huge variety of plug-ins allow fubar to display useful information. The ones I'm currently using include MoneyFu, PerformanceFu, ProfessionsFu, DurabilityFu, GarbageFu, ClockFu and BagFu. They're fairly self-explanatory, and you can find plenty more by searching for 'fubar_' A lot of people recommend using databroker addons as a successor to FuBar but I've never managed to get broker addons working properly so I'm sticking with FuBar for now.
2. Tourguide + Tomtom
Tourguide is a questing addon designed to provide a streamlined series of quests to do in the most efficient order. Combine this with Tomtom, which produces an arrow to tell you which direction to run in, and levelling is a snap. Equally as useful is the version of Tourguide for Refer-a-Friend we have been using that was linked from dual-boxing.com. The files to use are hosted here. I'd also recommend using the addon SilverDragon if you're doing the RaF version - we spent ages trying to find rare mobs and SilverDragon can help you to locate them.
Puts all your bags into one window. There are quite a few different mods that will do the same thing, but what I especially like about Bagnon is that it has a search function - you can search by name for items in your bags. Of course, Leesah still only has two small bags so it's not super-useful yet but it will be, ohh it will be.
Awesome for showing areas on the map where you haven't been and dungeon maps. I also pair this with Gatherer, which records where you find herbs, mining nodes etc for future gathering trips. Note: There is another version called Cartographer 3.0, which is an "experimental" version looking a lot like Google Maps. It completely replaces the Blizzard map, it doesn't work with the Blizzard quest indicators and it doesn't green-out areas you haven't explored. Looks nice though.
5. Prat 3
Prat is a great addon for your chat window. It colours channels, colours people's names according to their class, allows scrolling with the mouse wheel, makes channels sticky so you don't have to keep typing /g all the time... and that's just for starters! There are a bunch of different addons altering the chat window but this one is the first one I found that does all the things I'd like it to. (Bit of a retro screenie here)
The last addon I'd like to mention is QBar. All it does is add an extra action bar that contains quest items if you have any, so that you don't have to go searching through your bag for them. Really, really useful.
If you download the addon manually, you need to locate where on your hard drive your World of Warcraft folder is. In that folder should be an Interface\AddOns folder. Open the zip file you downloaded for the addon, and unzip into that AddOns directory. You don't need to create any new folders. Voila, start up your game and the addon should load! You can also download clients such as the curse client, that will help you to locate and install addons, and also update them when new versions are available.
Are there any addons that you can't level without? Leave a comment and let me know :)