How about some surreal stuff?
This AMV is made for old classic anime movie Paprika. Song is "Dreams" by Beck. This is just a good mix of both amazing anime and good music. Song isn't exactly following the action, but in this case, it's more about the general feel of it all coming together.
Now, this one is... is... Well, anime is Black Butler, which I dislike with strong passion. And music is... ready?.. "Be Our Guest" from Disney cartoon Beauty And The Beast. Yes. And oh my fucking god, it's not only perfect, it made me laugh, which says a lot. Matched to the pace and the lyrics, this AMV alone makes knowing that anime worth it.