1) To shit a someone's mouth while receiving a rim job
2) To have a ball rotate around a hole as if it was going to go in, but then suddenly it "jumps out".
"You better get outta there or I'm gonna rim out."
"Dude Sally was giving me a rim job last night and I rimmed out all over her face!"
"I almost sank a 30 foot putt, but then it rimmed out."