It's perhaps a bit of an odd assortment, but here we go.
NHL: Philadelphia Flyers. After moving to Connecticut, USA in 2001, I made friends with a HUGE hockey fan who gave me an NHL game for my birthday. The only teams I'd ever heard of were his Detroit Red Wings, and the Flyers, because they had been mentioned in a Simpson's episode (A Member of Satan/Flanders "Jury of the Damned). I thought it'd be more interesting if I supported a team other than my friends favourite, so I decided to follow the Flyers. I've been an obsessive fan ever since, regularly staying up till about 3am every other night to watch them live here in the UK
MLB: Phillies, Yankees. Because I lived in Connecticut for two years, I was in the heart of Yankees country. The very first sporting event I ever went to was a Yankees game a couple of weeks after I got to the US. I have a fondness for the Phillies because of my love for the Flyers
NFL: Eagles. Same reason as Phillies. I love the Flyers so much, some of that love spills over onto other Philadelphia Teams.
Scottish Premiership (Football): Heart of Midlothian. I was actually a Manchester United fan till I moved to the US from the UK, but being about 10 when I moved, I just liked them because they were the best. Living in America for two years, it was difficult to follow or watch them and I'd fallen in love with American sports that I stopped supporting them. A few years after coming back from the US, my Dad (a massive Hearts fan) offered to take me to a Hearts game as we were in Edinburgh (Hearts home town). I was curious, having never been to a football game before and agreed to go. Within 10 minutes of kick off, I was wrapped up in the amazing atmosphere of the stadium; it was nothing like anything I'd experienced at the Hockey and Baseball games I went to in America. I already knew by half time that I wanted to be a Hearts supporter and have been for the past 7 topsy-turvy years.
Sorry for the long post, but the reason I support my teams usually have stories to them which I like to tell.