Still one of the best AMVs (hit over 4 million views in it's first Youtube posting:
AMV:
She's Just Oblivious
Anime:
The Melancholy of Haruhi Suzumiya
Song:
Sharada
Artist:
Skye Sweetnam
An rather old AMV but still very good:
AMV:
Ranma vs Ryouga
Anime:
Ranma 1/2
Song:
Harder, Better, Faster, Stronger
Artist:
Daft Punk
An official Ranma 1/2 AMV:
AMV:
Wo De Airen
Anime:
Ranma 1/2
Song:
Wo De Airen
Artist:
Shampoo's Voice Actress
Ranma 1/2 has quite a few really good AMVs. This one sums up the romance pretty well:
AMV: Ranma is a Beautiful Disaster
Anime: Ranma 1/2
Song: Beautiful Disaster
Artist: Kelly Clarkson
Yet another classic Ranma AMV:
AMV: Nabiki Tendo
Anime: Ranma 1/2
Song: Material Girl
Artist: Madonna
A good comedic one, although I think this song and anime could handle a serious version as well:
AMV:
Fumuffu!
Anime:
Full Metal Panic
Song:
Holding Out For A Hero
Artist:
Bonnie Tyler
My current favorite is this one:
AMV:
Mahou Shoujo Requim
Anime:
Madoka Magica
Song:
Cosmic Love
Artist:
Florence and the Machine
To bad I couldn't find "Send Me Belldandy" the first AMV I saw that was really good. Youtube took the account down though, so it's no longer available. It set the anime "Oh My Goddess" to the extended 12" track of "Send Me an Angel" by Real Life.