I've seen so many concerts by so many different artists that it's hard to label a single one as "best gig I've ever seen". They're just too different to compare.
If I have to make a top 5 of different artists I think I'll go for:
1) Dire Straits, Feyenoord Stadium Rotterdam, 1992 - my first concert ever, I was 15 years old and saw my (still) favourite band in a sold out stadium with over 50.000 people. Still gives me a chill 20 years later...
2) Pearl Jam, Nijmegen 2007 - my favourite band of recent years (though I've been a fan since the Ten album), this was the first PJ concert I've been to. Since then I've seen them 3 more times (even went to Dublin to see them), and I'm adding a 5th and 6th concert to my list tomorrow and wednesday
3) K's Choice, Utrecht 2010 - another one of my favourites from the 1990's, also the first time I saw them live. Although their last albums don't rock as hard as their first 2 or 3 they play a pretty rough live set
4) Marike Jager, Nijmegen 2006 - a nowadays pretty well-known Dutch singer/songwriter, but when I saw her for the first time live it was on a stage in the backroom of a small music bar, with about 50-70 people. The small, intimate setting of that gig was a very magical feeling.
5) Dynamo Open Air festival, Eindhoven 1997 - I'm cheating a bit here, but this was my first big metal festival, and I've got so many good memories about the whole festival and all the bands that I've seen there, that I see this as a single (though very long) concert