Anywho...the shoe manufacturers of course say not to wash the shoes. But, I have a feeling that's the same thing as a 100% polyester shirt with a tag that says "Dry Clean Only." I think the shoe companies are just playing it safe. Seems to me that if you run in a downpour and your shoes get sopping wet, how is that any different than you washing your shoes. I've washed my shoes for years.
The main reason is that I'm a heavy sweater. My feet often slosh in my shoes after a summer run. My shoes don't stink from fungus or athlete's foot, but they do get this pungent sweaty smell. At first I would just remove the insoles and rinse them out with cold water. Then I'd take them outside and shake as much water out as I could and then let them air dry. For me, however, this didn't always take care of that sweaty smell. So I started using mild detergents like Woolite. That really helped. Most recently I've been washing my shoes in the washing machine in cold water with the new sports detergent WIN that's designed to remove sports-related body odors. My shoes come out fine.
I think the trick is to use a mild soap, cold water, and to let the shoes air dry. Never dry the shoes in the dryer. That can shrink your shoes or even melt the rubber if you use heat. My experience washing my running shoes of course is not scientific, but it's worked for me. My shoes run fine after being washed. If you're curious, I recommend taking an older pair of your running shoes and do a test wash. Then if they don't come out as expected, you were going to replace them soon anyway.
If you have any other tips/tricks for cleaning your running shoes, I'd love to hear them!