It's really hard to pick one as my all-time favorite, there have been so many great concert-experiences for me. Lumsk, Therion, Danko Jones, Hopalong Knut, Nightwish, Gåte and more have all blown my mind away during live shows. But I think I will go with the second time I saw Lumsk. The first time I saw them was at the Inferno Festival, and I had heard good things about them as well as listened to a song or two. They became one of my favorite bands that night. The second time they had changed vocalist and I had listened to them a lot, and they were playing this small venue in Lillehammer. Like downstairs a pub, hardly bigger than a livingroom, but a great venue since the guy booking bands had bot connections and an excellent taste. Anyways, we can't have been more than 10-15 people in the crowd, but Lumsk delivered an amazing concert anyways. And since everybody was standing more or less on top of the band (no barriers, and the stage was elevated about 20 cm if that) the connection between the band and the crowd was amazing. I think every guy in the crowd had a crush on the singer during the concert, she really managed to connect with the crowd on that night.
The worst moment during a concert was when my then-favorite band Dimmu Borgir butchered my favorite song by them during their encore. It was an older song, which they didn't play live anymore, but there had been talk that they would do some of the older songs from my favorite album. And they did, but some speeded up version that stripped the songs of what made them so unique and special to me. It was awful. Up to that point the concert had been good though, so more of a moment than a whole concert though.