If your washer pumps out the water but doesn't spin, check these:
The lid switch may be defective. If it is, the washing machine doesn't spin. The switch is inside the washing machine main housing near the door frame. Often you have to raise or open the top or front of the washing machine to get to the switch. If it's defective, you need to replace it.
The motor coupler may be broken. Many Whirlpool®-manufactured washers use a small, relatively inexpensive motor coupling. It's plastic and rubber and is mounted to the shaft of the motor on one side, and to the transmission on the other. Over time, the coupler wears out and fails. You may need to replace it.
A belt may be broken. Many washing machines have one or two belts. If a belt is broken or badly worn, you need to replace it with a genuine belt from the manufacturer. (Some washing machine belts are designed with special characteristics not found in automotive belts.)
The clutch may be worn. If your washer is a GE, it may use a clutch to come up to the proper spin speed. As the clutch wears out, it may prevent the unit from spinning well or at all. If the clutch is worn, you need to replace it. For this job, you probably want to hire a qualified appliance repair technician.
The drive motor may be defective. Many washer brands use a reversing motor. For agitation the motor runs in one direction, for spinning and draining, the other. It's possible for a motor to burn out in one direction and continue to operate in the other. If this happens, you need to replace the entire motor.
The transmission may not be shifting properly. Older washers produced by Whirlpool® have a transmission with an electro-mechanical shifter. If the shifter becomes even partially defective, the unit may drain the water but not spin. This is a complex system, if your washer has a shifter problem, you may want to hire a qualified appliance repair technician to repair it.
The spin bearing or basket drive may be worn or seized. These components allow the inner tub to spin freely inside the outer tub. When this is the problem, you usually hear a loud sound during the spin cycle. Call a qualified appliance repair technician.