My most unique concert, if you could call it that, was seeing very early Sublime and No Doubt play a backyard party at a friends house when I was in high school. I saw them both a couple more times at small venues before they got big.
I went to 5 Rage Against the Machine concerts but my favorite was my first in probably 95-96 sometime. Small place in LA standing room only. Just awesome.
Jay-Z and Coldplay at Wembley stadium was a cool one.
Diana Krall at Royal Albert Hall was great.
Jamie Cullum at Ronnie Scotts.
My friend worked with Blink182 from the very early days so I went to a lot of small shows in San Diego back when their music was fun and way less pop.