My Kenmore washer seems like the agitator is slipping during the wash cycle (it makes a grinding sound) and it won't spin the clothes during the spin cycle. It seems to pump the water out fine, it just doesn't spin. Can anyone give me an idea of what the problem is?

Could be a loose belt but more than likely the transmission has bit the dust. Years ago they used to have a WIG-WAG selonoid setup that could also cause that problem.