Once upon a time (otherwise known as “August 2013”), one nonnie linked to a tournament on another site in which people nominated and voted for their favorite songs used in anime. Discussion of this led to the idea of doing the same thing on FFA. The first FFA Anime Music Tournament proved to be so popular that it was followed by a second and then one for video game music.
The first AMT opened nominations on August 25, 2013, and ran from August 29th, 2013, to February 10, 2014. The final four were “Inner Universe” from Ghost in the Shell: Stand Alone Complex, “Duvet” from Serial Experiments Lain, “1/3 no Junjou na Kanjou” from Rurouni Kenshin, and “Magia” from Puella Magi Madoka Magica, and the ultimate winner was “1/3 no Junjou na Kanjou.”
Low-grade wank over people's taste in music brewed pretty much throughout the tournament; the biggest eruption came when "Blue" from //Cowboy Bebop//, whose soundtrack is widely considered among the best, lost to "Moon Revenge" from Sailor Moon. The tournament-runner was inspired by this to institute a new rule about not saying that you don't understand how anyone could legitimately like any given song (though of course this was unenforceable).
The first AMT also spawned the minor meme-meme of referring to respected anime music composer Yoko Kanno (of Cowboy Bebop, among other things) as “the Dark Lord Yoko Kanno,” as she had more songs in the tournament than any other individual composer and was considered to be difficult to beat, making any non-Kanno song that went up against her the scrappy underdog hero trying to topple the evil empire. (And indeed, in the end she only made it to the semifinal.)
The full slate of songs can be found here.
As soon as the first AMT began, people remembered various songs that they would have liked to nominate but had forgotten until it was too late. A second AMT was created for these songs–any song which had appeared in the first AMT was disqualified. The second AMT ran from April 14, 2014, to July 23, 2014; the final four were “Anna ni Issho Datta no ni” from Gundam Seed, “Kiseki no Umi” from Record of Lodoss War, “Zoetrope” from Amnesia, and “Sora” from Escaflowne: The Movie, and “Kiseki no Umi” won the day.
The second AMT garnered somewhat less attention than the first, but also less wank.
The full slate of songs can be found here.
The VGMT (pretty much the same as the AMT, but for video game music) opened nominations on August 19, 2014, to great enthusiasm; it garnered a total of 533 nominations, more than twice as many as previous tournaments. As of August 2015, it was still ongoing.