Oh yes, I certainly have "shower ideas" and I usually actively cultivate them. Sometimes its actually in the shower but other times it's while I'm mowing grass. It happens enough that I've grown to depend on it and use it purposefully - "I can't figure this out so I'm going to not think about it and go mow grass."

The trick is you have to stop trying to solve the problem and just let your brain work on it in the background.