I was two minutes late when My Chemical Romance was singing at Projekt Revolution... and I left five minutes before my girlfriend tracked down Matt Cortez (he's not technically in the band, but he's their #1 guitar tech and he substituted when Mikey Way left the band and got married during the past four months).
I've met plenty of great bands though, so I can't really complain (festivals like PR and Warped are great in that aspect), it just sucks because My Chem (especially Frank) are sticklers for signing/ talking to fans after nearly every show.
EDIT: Although I did kind of meet Matthew Bellamy of Muse... when they were touring with MCR in North America last year, this girl had a seizure at the beginning of MCRs set. I picked her up and ran her to the EMS room, which as it turns out was back stage. I run into the guy and just go, "I'm sorry man, my bad- oh my God, you're Matthew Bellamy!" But I didn't really have time to talk, given the girl and all...