My most memorable was Bono, lead singer of U2, of course. Met whilst staying at the hotel the band owns in Dublin, during a late night clubbing in the attached club. He proceeded to dance with and hit on my older sister

even though I'm fairly certain he's married!
I've also met Matt Wertz, a lesser-known singer.
Does being pushed out of the way by bodyguards for Jermaine Dupri and Janet Jackson at Derby while I stood in awe of them count as meeting them?