I am the Great Class Apostate. I don't like character classes -- I think they make RPGs demonstrably worse. I have a couple decades of play/GM experience backing me up, along with a track record of successful D&D class design, so I speak with some knowledge. And I'm badly outnumbered.
The upcoming D&D 5e will have character classes. That's one of the few things we know for sure. Nobody but me (and a handful of Google+ strangers) seems to mind. So be it. Rather than fight about it right now, I thought I'd try to do something useful. Here's a handy taxomony that answers the question: What do we talk about when we talk about "character classes"?
We're talking about the mechanical way(s) that a player is allowed to build a character, and the mechanical way(s) that a character is allowed to evolve over time. This sometimes overlaps with "race," especially in D&D and its immediate cousins. The difference is that race is generally a one-time set of modifiers applied during creation, while classes continue to direct the character's mechanical development. We're talking about this:
1) Class Systems: These lock a character into a set of game-specific mechanics that direct their interaction with their environments. D&D is the classic example, especially the earliest versions and 4e. You get a little flexibility with 3e's easy multiclassing and numerous prestige classes. Another once-popular game with a class system was Vampire: The Masquerade. Its clans look like races at first, but your clan choice dictates a great deal of your mechanical development.
2) Freeform Systems: These are the opposite of class systems; they allow characters to advance mechanically in whatever direction the player wishes. Freeform systems are often point-based, at least for character advancement. The most freeform system I can think of is Champions. Another excellent example (and my other favorite superhero game) is the FASERIP system for the old Marvel Super Heroes game.
3) Career Systems: Common to skill-based games, the career system encourages characters to follow paths by rewarding them for successful attempts at Doing Stuff or having them emphasize particular kinds of Stuff-Doing. A great example is Call of Cthulhu. Another one is the Fallout RPG series, with its Tag Skills (a mechanic that I'm surprised more games don't use). Yet a third is the original form of Paranoia.
4) Template Systems: They look like class systems on the surface, but they're freeform underneath. In a template system, you're offered several 'sample' characters with easy paths to follow. However, if you want to veer off the beaten track and manipulate the mechanics to your liking, the game won't stop you. West End's Star Wars does it just like that, with its ~15 model characters built on a super-easy system. Another system such game is 7th Sea. And Cyberpunk almost gets there. If you follow my lead on how I hack it, you can easily turn the game into a Role-free template-based experience.
Of them all, I think template systems are the way to go. They allow people like me to make whatever the heck we want, and people like [whatever you people are like] to stay within the security of predetermined roles. Did I miss anything?