For those interested, Kirk and Spock were the inspiration for the whole "slash" genre. In fact that's where the term "slash" came from. The writers who wrote about Kirk and Spock being lovers called such stories "Kirk/Spock" - notice Kirk "slash" Spock?
As time passed "Slash" came to mean any fanfiction that created a romance between two characters of the same gender, who weren't gay in the original concept. For instance you have Starsky/Hutch slash, but if you wrote about the two characters from Brokeback Mountain - or about two guys from Queer as Folk - that's not slash because they're already gay.
Fan fiction is full of fun subgenres, such as hurt/comfort (what it sounds like: one character gets shot, stabbed, sick, etc., and his best buddy worries about him and helps him out. Not slashy, though. "The Empath" is a good example of hurt/comfort, both Kirk and McCoy get bashed and comforted in that one) and stranger subgenres like mpreg (a male character gets pregnant. Personally, I don't get it, but to each his own.)
"Mary Sues" are very popular, that's when a female writer injects herself into a story by creating a female character who is sparkling, witty, super smart, and impresses all the men with her beauty and intelligence - and of course, the hero falls in love with her.
Before you ask - yes, I've written fanfiction. No, I don't write slash, it's all "gen" (the term for any fic that isn't slash). Horatio Hornblower and the Magnificent Seven television series, mostly. I don't write it anymore, but it was a ton of fun and a great way to learn all about writing because interested fans read your stuff and give you feedback. It's a good thing the Internet didn't exist when I was in high school, though, because I wrote some truly gawdawful 'Battlestar Galactica' fan fiction and I'd die if it ever got read now!! Poor Starbuck, I must have killed him twenty times...