My favorite is definately the Andy Warhol Museum in Pittsburgh.  I have been a fan of his art for many years and when I finally got to visit it, I had an absolute blast.
Oh, I almost forgot the Lace Museum in Brugges, in Belgium.  I'm a girl...  I like lace...  And it was absolutely amazing.  
I also love architecture and although they aren't really museums, I have visited quite a few of Frank Loyd Wright's houses and buildings as well as a couple others designed by some of his students.  I visited Falling Water in Ohiopyle, PA, the Guggenheim in NY, an other house designed by him in Ohiopyle that has no name and another cool building in Buffallo.
I especially like to visit old buildings.  When I went to Europe two years ago, that's what we did most of the time, visit old places...
Sophie.