Here is a link that might be useful:
Cleaning Running Shoes
I have put running shoes in the washer; usually they came out fine, but every now and then I've had soles that delaminated slightly. Whatever you do, don't put the shoes in the dryer. Makes 'em stiff as a board.
When washing your shoes in the machine, it's best to wash a few other heavy items like towels and jeans at the same time, so that the load won't become unbalanced (this makes dreadful wham-bam-thump noises and can damage the washing machine.)