A well used (and therefore wet) condom that a male discovers on his penis once he awakens from post-coital slumber. A wet hat typically results from a particularly aggressive sexcapade, which causes the male to collapse into a slumber immediately after ejaculating but before he has the chance to remove his spunk filled, vaginally lubricated scabbard.
Jon: I was fucked up on a lot of tequila and triple sec last night and ended up boning the hell out of Kate a few times. I think we ended up using a bunch of rubbers and the rest of my xtc, too.
Joe: Fuck! Did you have to cuddle afterwards?
Jon: Nah, I got pretty lucky -- I totally fell asleep right away. But I did have to deal with a wet hat in the morning.