There are too many to choose from for me, so I'll put up a few of my favorites. As with most AMVs, spoilers ahead.
Fun
Skittles
Anime: The Melancholy of Haruhi Suzimiya
Song: Candy Pop
Amazing Higurashi (Couldn't find original name. All I know is its Korean.)
Anime: Higurashi no Naku Koro ni
Song: Chu Chu Lovely Muni Muni Mura Mura Purin Purin Boron Nururu Rero Rero
HUGE SPOILERS
This is the updated version that actually got rid of some of the worst spoilers, but its still pretty bad. Another large portion of spoilers can be skipped by starting to watch at 2:20. Overall, not recommended at all if you haven't seen the show and may want to at any point in the future. Knights of Fate
Anime: Fate/stay night
Song: Knights of Cydonia
Wow, Order, I really have to disagree. Even ignoring my extreme dislike for Naruto, I still have to say that that was terrible. So bad that not only did I really not enjoy it, but I had to stop halfway through due excessive eye strain and a headache that it caused.
The only real effects used were blurring and flashing (of either a solid color or random, meaningless objects). Both were used poorly. The only real point to blurring is to either get you to focus on a single thing that is left unblurred or to blur a single thing to keep its details hidden. The creator of this video often would just blur the whole screen for no apparent reason. The few times he didn't blur the whole screen, it was either hard to tell what was unblurred, the object in focus was unimportant, or in extremely rare cases, the blur actually was used well, but added little to the video.
Then he quickly flashed things in a way that it is painful to watch, and again serves no real purpose. Sure, it has decent syncing to the music, but it adds nothing to the video and actually makes the video worse.
Then there is the poor quality sources he used. Which isn't even consistent. Sometimes we get the DivX logo, sometimes we get unimportant and sometimes distracting subs, and even a couple times we got TL notes.
tl;dr
Poor quality source + No beneficial editing + Random blurs and flashing = Not a very good AMV
Not only terrible, imo, but painful.
@Rusteh: AMV Hells FTW! Not my favorites really, since they just don't have the quality that standalone AMVs can have, but they are always really enjoyable. Personal favorite is 3, though a few of the minis might be able to match it.
It's not the act of doing it, but the correlation I draw with mentally "less gifted" people on Twitter and hashtags. When I see people hashtag, it is commonly on pointless, idiotic, dumb, or just plain incorrect things. So, that's my thought process.