Of course, there's been an equal amount of ridiculous and sublime in the various attempts to reinvent cameras and photography, but no one can say that manufacturers aren't trying.
So, I present for your amusement, in no particular order, my picks for the 20 most interesting cameras I've seen in 2013, plus one bonus model which I'll probably never see, because it's not meant to cross the US border. These are neither the best nor the worst products I've encountered, nor have I gotten to test some of them yet. They're simply all notable for their contributions, for good or ill, to making cameras fun to cover in 2013. Have I forgotten any? Note them in the comments.