I used to watch AMVs all the time, back before some of y'all were born I'd wager. It was such a cool thing, we'd show them during our Anime club, and trade VHS tapes filled with them. It's a shame that some of my favorites are likely lost to time. I've been looking for Duane Johnson's "World I Know" set to Wings of Honneamise forever. Still can't find it.
The thing that old videos, well the good ones anyway, were able to do I think better than a lot of modern ones was nail tone, and tell a story. You had to plan shit out far in advance, especially in the 2 VCR days, Premiere made life easier, but it also opened the floodgates of crap, nowadays it is damn hard to find the great ones. I'll be checking out some of the ones in this thread.
Anyhow, some old classics:
The Phantom of the Opera - Memories
This video is just great, 90s as hell, but a great mix of the song, and great use of visuals.
Sarah Brightman - Once in a Lifetime - El Hazard
When I was in college this was considered one of the greats. It also introduced me to Sarah Brightman, something for which I am eternally grateful. It does a great job of telling the main story of El Hazard in just a few minutes, and it just works. Think this is just a 2 VCR vid too. Crazy.
Lorena McKennit - Mummer's Dance - Princess Mononoke
Music fits the anime perfectly, I think this was around the time that people started using software to edit videos. Blew my mind the first time I saw it.
Of course the 1990s were so awesome, we had professional AMVs that played on MTV:
Matthew Sweet - I've Been Waiting
First time I ever saw Lum, I fell in love, and have yet to fall out of it.
And a modern one I really like:
Regulate - Black Lagoon