Just about everyone has an idea of what classes should be. Some people prefer them to be very wide and far reaching, with as few classes as possible but perhaps lots of sub-classes, kits or whatever you have in your game to differentiate members of the classes. Others want to have as many classes as you have different roles in the game world; "cleric" could be a class, but so could be "priest", "shaman", "monastic" and what have you. Personally, I think these aren't necessarily opposed actually.
One idea I've toyed with, but didn't really finish was a derivative game out of DCC RPG. In that system, characters would choose one of three possible, very generic classes. Each of these classes would represent one of the important gameplay aspects out of this kind of game; a "fighter" class would be focused on combat (in all the forms it might take in the game, such as one on one, group combat, mass combat, etc), a "magic user" class that would focus on... well, magic, and an "explorer" or "thief" class that would focus on the exploration aspect of the game. Note that these three are particularly geared to the kind of game D&D is. Games with focus on different activities could have different classes as well. In particular, a game like Shadowrun would justify there being a "face" class, that would focus in social interaction and manipulation. A game like CoC would justify an investigator class, since gathering clues is a very important activity in those, etc.
The point here is that these classes aren't concrete parts of the setting. They are abstract aspects of the gameplay the game and the DM has in mind. Which is why they are given rather generic names. Their implementation is likewise, abstract. Having a class and levels in it wouldn't, in this system, actually give you any kind of concrete ability. You don't get sword proficiency for being a level 6 fighter, for instance. Nor do you get access to new spells for levelling up as a magic-user, neither does your explorer class give you access to a disarm traps skill. Rather, these classes would give you bonuses and safety nets for doing abilities that are within their domain. A level 4 fighter might, for instance, re-roll a failed attack roll twice a day. While a level 5 magic user might be able to avoid a critical failure for casting a level 3 spell once per day.
