These have both been mentioned around here, but I have two, really.
First, the first night I saw Porcupine Tree, on their Deadwing Tour. I believe Keithb might have been with me, but I was pretty entranced by what was going down on stage so I wouldn't stake my life on that.
Anyway, they played "Arriving Somewhere (but not here)" which hadn't really blown me away on the album, but between the video behind the band and an amazingly intense performance, I was floored. So was the crowd - it was at the Berklee Center for Performance Arts so everyone was seated, but as the final chords faded everyone erupted into applause and started getting to their feet, and it turned into something like a 2-minute standing ovation in the middle of their set.
The other concert highlight for me was catching the Charlie Hunter Quintet as part of a weekly jazz concert series at the Clark Art Institute in Williamstown. 99.5% of the crowd were probably in their 80's, leaving maybe another 3-4 guys roughly my age, myself, and my dad. It was nuts - these guys were grooving their asses
off on stage, and the crowd was just sitting there in shocked silence - they'd clearly been expecting something more like Benny Goodman than Charlie Hunter.
The band looked like they didn't quite know what to do (and even alluded a couple times to how this wasn't the sort of venue they were used to) but still managed to play with the sort of energy you usually only see at rock shows. The double bonus here was that it was the first non-classical concert my dad had been to since before I was born, so it was cool to be there with him.