I'm now to the point where I can play ~25 champions very effectively.
So far the champions I feel the most useful as are Blitzcrank, Cho'Gath, and Nasus.
The rest of the champions are very dependent on your team synergy and whether or not your teammates are >60 IQ. Playing carries is fun end game, but if your team screws up bad early game or mid game then the carries never reach their full potential, while Blitzcrank is useful at any level, any part of the game, regardless of how well you're doing.
Gonna try getting good with Annie next after she waltzed into my lane last night, only 1 level above me and my lane partner, and proceeded to double kill us without effort.