I've been fortunate to go to so many great concerts. Luckly liking smaller bands = cheaper tickets lol! I'd have to say the best show I've ever been to though was Neutral Milk Hotel a couple years back. I went to California to see them 2 different nights and I got to go to Disneyland and the beach while I was there. My best friend went along and when I saw them the first night I got front row seats, they played an honest unplanned encore (I managed to snag a setlist too!), and I was able to hang around and briefly meet all the members of the band after the show. It was really such a dream come true.
I'll echo everyone saying NIN is incredible to see live! I've been lucky enough to see them twice now, They were the second concert I had ever been to and are probably the main reason why I'm such a concert junkie today!
Spoiler
First concert I ever went to was Cher when I was in grade school. That was fun too, I remember my grandma bringing her binoculars so we could see from out super cheap seats :P
I've only ever gone to one show, not even a concert, but it was great. The main act was Fear Factory, one of my boyfriend's favorite bands, but I fell in love with one of the supporting acts, Soilworks, after hearing them play. It was pretty intimate since the venue was a small local club and the vibe was just perfect. According to my boyfriend the mosh pit was pretty awesome too but I stayed on the sidelines :P