Looking back, the first concert I ever went to was probably the worst--Bush with Veruca Salt back in the mid 1990s.
I've been to three concerts that really stick with me. One is the Kenny Chesney/Tim McGraw double bill I went to with some girlfriends from high school once we were all in college. It was at the Rose Garden in Portland, which is a terrible place to see a concert if the act in question doesn't know how to connect with the audience (see worst concert, above). Even if you don't care for country music, Tim McGraw puts on an amazing show. We had seats at the back of the arena, and during the intro of his band, the Dancehall Doctors, we were waiting impatiently to spot Tim coming on to the stage. Suddenly, the lights went down except for a spotlight on an area a couple rows from where we were, and Tim appeared out of a giant equipment case on a stool as the band launched into Elton John's "Tiny Dancer." Seeing him perform that song so close to us was truly cool.
I've also been to a couple of outdoor shows that were great: Pink Martini at the Oregon Zoo (awesome band, amazing venue, fun times, and a quintessential Oregon experience, in my mind) and Floater at the Cuthbert Amphitheater in Eugene. For the latter show we had a great big group of people (mostly old college buddies) and were able to commandeer a large plot of grass for our party with a great view of the stage. Not only was Floater great (they usually are), but they had a really interesting opening act, That 1 Guy: