What class-and-level system increases the breadth or variety of characters' abilities instead of the power (often in the form of bigger numbers) of their abilities? Such a system should have leveling up mean something other than gaining the ability to sustain more damage from foes and the ability to engage with the world using just bigger numbers.
For example, a system might have a fighter who at level 1 only swings a sword, but when he gains a level he can trip foes. His ability to swing a sword and trip his foes, however, remains static throughout his career.
The wider and weirder the variety the better. For example, a system in which a fighter who begins as a sword-swinging brute can take a level of wizard to cast spells then take a level of rogue to sneak around then take a level of cleric to blessed by the gods and so on is preferred over a system in which a fighter can only gain levels to get different methods of mundane fighting.