About 10 years ago I was working at a Jiffy Lube when a guy came in with a V6 Passat. He said he added oil until it was full and it started running bad.
Turns out, his idea of full was adding until he saw oil up to the fill hole.
The car was still running, somehow, though VERY sluggishly. I actually don't remember it smoking much. If I remember right the manager agreed to drain out the excess if the guy signed a waiver or something like that. The car seemed to run fine once the excess oil was drained out.
That was by far the most severe case of overfilling I have seen in person.