I often insist on the fighter, magic user and thief as the core classes of Dungeons & Dragons, since each of them has a unique mechanical subsystem. It’s been pointed out to me, though, that the cleric has his own subsystem, too: turning.
So I think it’s reasonable to define a core class, in non-Advanced D&D, as a character type which owns a unique subsystem. That gives you the core four. It’s also a rather elegant guideline for when to create new core classes, versus when you should extend a previous class.
As I develop my all-new Sorcerer class (details soon), I’ll be keeping that in mind.
And wait ’til you see where that ties into Vampire.