RPM's increase drastically but car doesn't accelerate

I notice this mainly when I'm running my air conditioner or going up a hill; If I press down on the gas pedal, the engine will surge in RPM's but there is no corresponding increase in speed or power from the engine (the engine revs but I don't feel a jerk like it's shifting gears). When I let up off the gas pedal, the engine returns to normal. I've talked to several people and gotten several different answers as to what the problem might be.