I'll put my money on some kind of moth? I'm no expert, so I can't ID it to the fine points, but I think it is some kind of Hairy Moth. Really, that's their name. Sorry I'm not able to give more details.

I found it by a lake near Branson, MO. Whatever it is, it can remain perfectly still for at least a day. I thought it had died on the window until I touched it with a leaf and it flew away.