AMVs, and some other fanvids, that I've liked. Some I think are genuinely good, or at least strongly appeal to me; others are listed out of collector-instinct, especially if they're technically impressive. I've tried to sort them, 'good' first in a category.
Link update 25 Sep 2016.
Not all links will work, as videos get deleted from Youtube, but I keep the text in hopes of finding them again.

Broad appeal (all good)

  • Every Anime Opening Ever Made
  • Right Now
  • Anime Munters Foe Yay
  • Ship Happens. Funny, and pretty painstakingly done if you watch carefully.
  • Chronicles of Ghibli
  • Soldier A. Original tribute to redshirts.
  • Lucky Me (Buffy romance) (not anime)
  • Golden Boy/I Want to Ride My Bicycle -- first AMV I liked; I liked it without knowing the sources, either the anime or Queen or the cover.
  • Princess Tutu Hold Me Now -- demonstrably works for people who haven't seen Tutu. Also, spoilery.
  • As above, with "disco" visual effects
  • Watchmanga (Watchmen, Darker Than Black, Cowboy Bebop)
  • Caramell Dansen misheard lyrics
  • Silence of the Vampires -- Hellsing cross Silence of the Lambs. I haven't seen either and liked it. OTOH I did know something about Hellsing.
  • Space Girl (not anime)
  • Fireflies, random cheerful melange
  • Complete History Of The Soviet Union, Arranged To The Melody Of Tetris
  • Touhou Bad Apple (silhouette)
  • Touhou Bad Apple (English subtitles) (silhouette)
  • Ballad of Mike Haggar
  • The Phantom Menance: How to fight with lightsabers
  • Chobits / The Internet is For Porn (broken)
  • We Need You various things to Starship Troopers. Should be good for all. (broken)

    I liked (so all good) but think you might need more specific background, but they don't need their own fandom categories

  • FMA "Date R*pe"
  • Utena Matrix
  • One-eyed fish, Mushi-shi AMV
  • TTGL x Mulan Also this (broken) is similar.
  • Sora no Woto Good Day to Die
  • Captain Harlock live action fan trailer
  • Cleaver Girl Higurashi's Rena to "Creepy Stalker Girl". Excellent, might be decent if you haven't seen it.
  • Lodoss war Saga begins
  • Evil Buffy opening (not anime)
  • Princess Tutu Caramelldansen -- with real dancing!
  • Princess Tutu "Extra Episode"
  • Macross Frontier Starship Troopers -- has no soul but very well executed.
  • Bleach 300 Trailer. There's a zillion of these, but this one features Kenpachi's 11th Squad as the Spartans, so it has a thematic unity most others lack. At least if you've seen enough Soul Society arc to get a feel for Kenpachi and his squad.
  • Hermione the Pirate Queen
  • Scrapped Princess: Me Against the World. 10/10 for theme. :)
  • Senshi on Springer
  • Wizard of Ozaka
  • Them Daleks Ain't So Scary
  • Torchwood Banned From Argo. Yeah the Torchwood crew would get themselves banned.
  • This Land Is Mine war video

    Haruhi Suzumiya

  • Harassment of Kyon -- Koizumi/Kyon/"I want to be your girlfriend"
  • Haruhi/She's Just Oblivious -- very well-matched if you know the series.
  • Ship Happens. Funny, and pretty painstakingly done if you watch carefully.
  • English AmaLee cover of God Knows
  • collector below
  • Tsuruya song

    Mahou Shoujo Madoka Magica

  • Fandubbed Magia, actually sounds like the original. (AmaLee)
  • Homura opening (fandub)
  • Doctor Whomura 1. Cute concept.
  • Doctor Whomura 2 (broken). Ask me in person.
  • Madoka/Homura cosplay stills outlining the story. Impressive.
  • Live-action cosplay at Anime Expo. Pretty good apart from the Homura's body language, more moe than badass.
  • Alternate Walpurgisnacht , pretty awesome. Version with subtitles. External interpretation.
  • Uninstall -- I've never seen Bokurano, but its OP apparently goes really well with Madoka.
  • Superhero
  • Homura Bad Apple (English) (Rebellion spoilers) Very well matched.
  • Bad Apple (English cover) slow, poignant, spoilers. I like the singing, I think it's less well crafted.
  • Bad Apple (original, high energy, subtitles) Homura centric, nightmarish visuals, decently matched.
  • Buffy style OP
  • collector below
  • Inception mashup. Cute concept.
  • God is a Girl. Okay video and song, but the title's so appropriate.
  • Melancholy of Homura Akemi. Tech impressive.
  • Homu Homu no naku koro ni. I like both sources, and they do match on creepiness.
  • "Season 2" OP, Suzumiya style (broken) Tech impressive.
  • How much are Homura's weapons worth? (broken)
  • Family Friendly Episode (broken)
  • Nowhere Land -- I like the music
  • If I could turn back time
  • Time After Time
  • Aozora Tears -- don't remember why I saved this
  • just plain surreal
  • Just A Dream (yuri fanart stills)
  • Come Little Children

    Twelve Kingdoms

  • Rakushin In Love With Two -- nice dual ship AMV.
  • 12 Kingdoms Caramell Dansen. Most complex Caramell I've seen, short of mis-heard lyrics.
  • 12K fanart slide -- slideshow of 12K fanarts, to the series music.
  • 12K -- Strength in Transformation. Evocative music.
  • Taiki's Nightmare. Likewise.
  • The Cost of the Crown -- set to a Lackey song
  • collector below
  • Shoukei's Song, English cover. Words start after a minute.
  • 12K Elizabeth -- nicely done, despite the plots have little to do with each other.
  • Youko's Mad World
  • 12K Avatar
  • 12K Taiki stolen child (broken in US). Taiki scenes to the Loreena McKennitt song.
  • Youko's Legend, crossed with Mermaid Melody and "30 Minutes" by t.A.T.u.

    Nanoha Lots of sappy NanoFate.

  • NanoFate in Heaven
  • Don't go Breaking My Heart NanoFate. Crude art style is appealing somehow.
  • NanoFate Summer Loving. Same style as above.
  • NanoFate Perfect Two with fanart slides and cute couplets.
  • collector below
  • Nanoha & Fate Give Me 30 Minutes. t.A.T.u. again. Pseudo-lesbian song for the hidden lesbians.
  • Nanoha -- I want a mom (broken)

    Mouretsu Pirates / Bodacious Space Pirates

  • collector below
  • Mouretsu Pirates -- you are a pirate
  • Mouretsu Johnny I hardly knew ya. Has some nice matchings in the first half.
  • Sky-pirates song -- cute/weird/appropriate music/song.
  • Hand of Sorrow
  • She's a Pirate (PotC "He's a Pirate" track)

    Anime Boys and (mostly) Merry Wives of Windsor

  • Gentleman Soldier
  • Anime Boys Twa Corbies
  • Anime Boys tribute to the Green Hills of France

    More random. If it was really good it'd be in the second group, but there might be amusement value.

  • Scrapped Princess: Vanity
  • Avatar -- Zuko brain damage -- kindof funny.
  • Top 50 Anime openings in 10 minutes
  • Haruhi S2 English Super Driver (broken)
  • Yu Yu Haksushou Buffy -- feels well done but I don't know the anime.
  • Villainous Destiny -- might work better if you know old anime to recognize the villains; I get Laputa and Lodoss, I think. (broken in US)
  • First non-sucky Buffy/Sailor Moon I saw (broken)
  • Cardcaptor agni kai (broken)
  • and in reverse
  • COPS GitS
  • Doctor/Master/Avenue Q (broken)
  • People's Mario
  • Commiedora
  • Communist Mario-Stalin
  • Azumanga Soviet
  • Banned cartoons (broken)
  • Minecraft Ghibli World
  • Girls und Panzer Katyusha
  • misheard lyrics
  • Anime's Got Talent
  • Dating Sim AMV
  • Safety Dance
  • Bebop/Trigun All that you can't leave behind -- saving mostly for the top notch editing.
  • Magical Girls/War Paint/Phoenix
  • Spice and Wolf / Fairytale
  • The Love Craft