If the machine is spinning as hard and fast as it should.... then I can only think that you have a problem with a plugged drain pipe.. (The one that the big hose in the back of the washer slips into.) If so, you'd need a plumber to help. Now, I'm assuming that you already know that if you end up having a severely unbalanced load, that it will kick out of the spin cycle prematurely, so that it won't shake itself to death... That would leave water in the machine.

If the washer cannot balance the load it will end after a period of trials but it will not be able to fully spin out all the water. It could be that the load is too much. try a smaller load. Also check your drain filter and clean it periodically. Be sure the washer is level and that it does not rock or move.