The only "class" you pick is warrior, mage, or thief. This can be changed at any time by visiting the sign stones. It just changes which of your skills levels faster.
I'm going to run with mage most of the game, but try to keep my sneak leveled. So I may switch over to thief every now and then.
You're going to be some kind of... Sneaky... Witch-thief!
Edit: Kudos if you get that reference.
Anyway, I was thinking that I wanted to play just as a Breton mage, which... I've never really stuck to just one class, before. But now I'm not sure... In all my other playthroughs in other TES games, I usually create one character that I really like, and I do every single quest with her, all the factions, and work on all my skills. Now I'm conflicted, though. I like exploring the world with my one character, but the Skyrim seems to be set up, I don't know, is it like New Vegas where if you choose one faction, you can't help another faction? It kind of seems that way...
This would be the first time that I actually roleplayed a character and kept that character doing just one thing... As a Breton mage, joining the mages guild, trying to avoid joining other guilds like the Thieves or the Dark Brotherhood... It allows me to create other characters (Like a Khajiit Thief, or a Bosmer Assassin, or a Nord Warrior) But I feel torn. I don't know which way to go. All these other people have their builds for several different characters laid out, and I'm kind of like... Lost. I guess it will be better when I get my hands on the game and can play it for the sheer enjoyment of playing it. I probably won't even worry about all that stuff at that point.