Did the ancient Romans have paddlewheel battle ships?
I just found a Wikipedia entry about paddlewheel-powered battle ships from the ancient Romans. It's not clear whether these ships ever were built, but at least there is a description of it in existance. Of course, they didn't have steam engines but were planing (or really did) using oxen for power.
See the details and a picture at Wikipedia: De Rebus Bellicis