I haven't really followed AMVs in years. Some of my favorites from way back were:
"Roseate Nocturne" from UtenaI swear, I'd never even heard of Evanescence at the time I first saw this. And unlike every video I've seen featuring them since, in this case the lyrics are not overly melodramatic - in this instance, for Anthy, they are
accurate. I have a whole folder of Utena videos but this is my favorite (probably of anything ever).
I also have a folder devoted to Cowboy Bebop videos, of which the most notable are
"Tainted Donuts" (which is a Bebop / Trigun crossover, and hilarious if you've seen both shows, but if you haven't you probably won't get it) and the impressive
Pulp Fiction which is *really* well timed, as well as a great introduction to the show.
While it suffers from being a Linkin Park song and everyone hates them now,
"Paranoia Rebirth" does a nice job at summing up Ayashi No Ceres (and is well timed). If you've never heard of it, this may give you some interesting guesses as to what the plot is about!
There's also a Key The Metal Idol video to Nine Inch Nail's
"Closer" (NSFW!!!!) which sums up the show, but with MASSIVE, MASSIVE spoilers. However, as I was kinda pissed off at that anime after finishing it, I would tend to recommend that you watch the video INSTEAD of the entire series. The AMV author was also extremely depressed and angry when making it, IIRC. Be warned, it is meant to be disturbing.
I also have a multiple-series AMV to "Come What May" which makes me
blub from the overdose of romantic angst. I'm a soft touch. However I couldn't possibly find that exact video on youtube, so you won't get to find out just how easy I am.

I used to download AMVs all the time and I only kept the ones I thought were awesome, so I have a decent collection of memorable ones, but I don't think you want to hear about ALL of them... do you?