Product review (5 stars): Kenmore Elite He 3t 4t 5t Washer water Pump - Right product, Right price.
I am personally not a big fan of getting bent over by a company when I buy a replacement part to fix their broken product. So after calling the service department for Kenmore and getting quoted just shy of $200 shipped for the whole pump assembly with the housing and stuff that I really didn't need (they wouldn't sell just the pump) I decided to look elsewhere.

Amazon=awesome.

The pump arrived and after about half an hour and with the assistance of a pair of pliers to undo the hose clamps and a screwdriver to take out half a dozen screws, the old pump was off and the new one was on.

It's been a couple of months now and it is still working like a champ.