Here's an AMV I found: http://www.youtube.com/watch?v=kg4j8o0XiBs
It's interesting in that the song itself is a mashup of various songs (that go pretty well together IMO). The video draws from a number of series as well as FMA (it uses the first series and the movie.) I think parts of the video could have lined up better with the music, but other parts clicked really well.
Viva la Vida by Coldplay,
When You Were Young by The Killers,
Because of You by Kelly Clarkson,
Livin' on a Prayer by Bon Jovi,
Walking on a Dream by Empire of the Sun,
Starlight by Muse,
and All of Your Love by Hellogoodbye.
and the video's from
Howl's Moving Castle
Final Fantasy VII (Advent Children, Crisis Core, and Dirge of Cerberus)
The Princess Bride
(I think it could've done without the live-action parts, they looked weird in comparison to the animation and CG.)