My Whirlpool Washing Machine Is Having Problems With The Spin Cycle, What Should I Do?

I have a 15 year-old Whirlpool washer. Lately, I've found standing
water and wet clothes in it after the cycle has finished.
Further info:
- If I let the cycle run normally from the beginning, it fills
normally, and the timer dial moves normally. It agitates normally,
then keeps on agitating through the rinse & spin cycles, and then
stops (without ever spinning) once the dial get to the end of the
cycle. If I turn the timer knob and position it back to the spin line
and engage it again, it will spin and drain just fine from there.
- If I let a cycle run from the beginning, then stop it when the dial
gets to rinse (by pressing in the timer knob and then pulling it back
out), it will go into spin mode right away and drain properly.
- If I let a cycle run from the beginning, then stop it when the dial
gets to rinse (by opening the lid and then closing it again), then it
will go into spin mode right away and drain properly.
- No change in these symptoms in any of the cycles (regular, heavy,
delicate, etc)
So, as long as I manually put it into a spin mode, it works fine. But
if the cycle just runs normally, then it just keeps agitating and
never spins or drains.
Any suggestions or ideas appreciated.

Probably has a broken belt or the belt has come off. Happened to us a few years back. You'll need to pull out the machine from the wall, remove the back plate and manually check to see if it is intact or not. If that is not the problem you may need to call a repair man and if it continues to happen- replace the machine altogether.
Good Luck- Auntimaime

It could be that the belt is broken.  I'm not sure what you mean when you say you have to manually spin it.  Do you mean you sort of kick start it to spin.  By that, I mean do you spin it until it starts spinning on its own, or do you manual spin it until your clothes are spun.  That would seem to be a little difficult if not impossible.  At any rate...this has happened to me twice.  The first time the belt was broken and was very easy to replace.  I looked up the directions on fixityourself.com.    The second time I had to unplug the machine and reach under the bottom of it, grab the belt and give it a firm turn.  Then I would plug it back in and it would spin.  I  finally got a new machine, fortunately. 

I too am having the same problem. 1st we had to replace the motor coupling. Then the agitator dogs cause they were stripped. Then I was having to lift the lid to make the washer spin. It would always drain. So we just changed the lid switch. The washer worked perfect for 2 days. Now today it won't spin unless I push the timer knob in then pull it back out. We have looked at the belt and it is fine. So I think it may be the transmission. But I'm no expert. Just thought it may help you narrow it down.

It's usually a broken lid switch.

Just a guess, but there could be something small like a sock, etc., stuck in your pump or the belt may be bad.
You would have to take the screws off the panel on the back of your washer to take a look at the belt and pump.
If the belt looks okay, then you may want to unplug your washer and remove the pump to see if it is clogged. It's usually not too difficult, just a couple of screws holding it in place. You will need to loosen the clamps on the water lines running to the pump also. Once you get the pump off, take it to your sink and run some water through one end to see if it flows out the other. If not, then it is probably clogged. Look in both ends to see if there is something stuck inside. 
If the pump is clear, you might want to check the water lines that connect to the pump.
If you continue to run your washer without checking, and it is a clogged pump or line, you could possibly ruin the pump.
Sorry I couldn't be of more help. It is difficult to diagnose a problem like this without actually looking at the washer.
I know that calling a repairman can sometimes be expensive, but in the end, you may have to.

If it's a top load machine it's probably the motor coupling.

My whirlpool washing machine is leaking and it is noisy on spin cycle mode

My whirlpool top loading washing machine spins only on regular cycle, will not work on any other cycles?????

Well this is problem in the wheel motor of your car that is making problem in your washing machine so you must fix it because it is not getting enough pressure to spin wheel of your machine.