I was born in Detroit, and my family, extended family and the friends my family hung around with were all big into hockey. I was born in 1986, so it was after the Wings turned the corner from being horrible and everyone was excited about Yzerman and the team being on the rise. There would be Red Wings watch parties at people's houses in my family's group of friends, so it was kind of always a part of my life, even if I don't remember those days so much, because I was young...
We moved away from Detroit to Cleveland when I was 4, there wasn't any other team to cheer for here during that time (well before Blue Jackets...). Most hockey fans in the area were Pens fans, because that was the Lemieux/Jagr era. I just stayed a Wings fan because of my ties to Detroit. My earliest memories of being a Wings fan is the 1994-95 and 1995-96 seasons. Losing in the finals to NJ and the start of the rivalry with Colorado, then seeing them win the Cup.
Not a terribly exciting story, I could have stopped at "I was born in Detroit" to answer the question, but figured I'd embellish on that. For all the other sports, I pretty much cheer for the Cleveland teams, because those were the games I was able to watch on TV growing up, so I am a Browns and Indians fan more so than Lions and Tigers, but I like seeing them do well too. I was actually a Dolphins fan for football growing up, for some reason, it was pretty much after the Browns left to go to Baltimore, and I think I just wanted to see Dan Marino win a Super Bowl because of how good he was. I really don't care about basketball. Michigan over Ohio State (ugh...). But the Wings are by far my #1 team.