You'll most notice weight when climbing hills. Big difference between your old gas-pipe 30lb Schwinn and a 20lb road conversion when you go up the same hill.

Rotational weight (the wheels) is more important and more easily felt than weight elsewhere on the bike. Than again, you also want wheels that will handle uneven surfaces and the occassional pothole/curb drop, so if you're 220lb it's probably not the best idea to get some 28 spoke Velocity Aeroheads...