Then there is the utilitraian Goat Fuck. This normally requires a serious amount of work to unfuck.
Lastly, there is the Goat Rodeo. The worst of the three, it is beyond even profanity. It describes a situation that involves many individuals screw ups, and implies that the fuck up is already well underway, meaning that there is no hope in stopping the mess. Usually said with a defeated tone:
"We had Ondine's fifth birthday party yesterday. What a goat rodeo!"