You know all that change, pens and other small things (like foam ear plugs) that disappear in your front-loading washing machine? No, me neither. However, it turns out that there is a trap before the pump. And when it gets too full of change, pens, ear plugs, hair, and other various pieces of plastic it can overflow and something can block the pump. In this case it was apparently a penny.
The good news is that it's fairly easy to clean out said trap and I don't need a new pump. The bad news is that vile things grow there and it smells bad.
Something to add to the list to clean when I'm cleaning out the dryer duct.