The Conan RPG system (noted as one possible "other"):
+1 feat at first level in that class, one at 5th level (again, in that class), and one at 10th level (again).
However, if this is done, I would say that a human or half-elf must choose one class (any class, but it must be chosen at first level) as their favored class.
Getting +1 feat at 1st, 5th, and 10th level above and beyond racial features is otherwise just overpowered.
As to classes being abstract...
Dwarves are (commonly) dedicated to being Fighters and very good at it. That should be represented beyond +1 x level hit points, +1 to Fortitude saves, +1 to a couple checks, and minor combat bonuses very specific enemies.
That's not "very good at it". That's "useful abilities".
Personally, I would like to make it so that each class represents a pretty hard-to-shift-from choice, with each class being a distinct set of abilities (though not necessarily unique).
Being a Barbarian/Fighter/Monk/Rogue can probably be justified (at least to the person making the arguement for such a character) if you try hard enough, but if we really want to build characters like that, I'm not sure how a class based system helps character creation at all.
Seperate discussion, however.