Spacebattles has had several huge fanfiction trends, most of which I’ve naturally missed.
-Star Trek/Wars/B5/BSG/Stargate fics. Waay back in the day. I entered just as those were fading. Mostly before my time, and Creative Writing was a relatively small, out of the way forum.
-Familiar of Zero. Already mentioned. Gained popularity because of its enormously crossover-friendly setup. Has since largely petered out.
-Self-inserts. Not an exact genre so much as a style of writing. Goes against everything a writer is supposed to do, but as a combination of wish-fulfillment and way to write in an established setting, it worked.
-Worm. This was a bit of a surprise. A long, obscure web-fiction about a superheroine, Worm’s fandom is concentrated on SB-but is very concentrated. Having read only a little, Worm’s draw of both “taking advantage of” superpowers and its surprisingly crossover-friendly nature (fanfic writers love to give the main character different powers) have earned it a huge following on the board.
-Time-loops. Lowest-common denominator goofball-fic. Basically, think Groundhog Day-styled stories. Add in characters of all the settings one could want. Huge needlessly complicated backstory and set of nominal rules. Ability to avoid such matters as plot, character development, or pacing by just rushing ahead to the goofy. (You get the feeling about my opinion on these).
As of the time of this writing on the Creative Writing front page:
Worm, Worm, Star Wars, Worm, Self-Insert, Worm, Loop, Loop, Mass Effect, Worm Self-Insert, Worm, My Little Pony, Worm, BSG, Self-Insert, Self-Insert, Worm, Self-Insert, Loop, Loop, Self-Insert, Loop, Loop, Pokemon, Stargate, goofy meme, Lord of the Rings, Self-Insert, Worm.