I grew up in Chicago and started following hockey then and there. I came of age in the late '80s - early '90s with the Roenick, Belfour, Chelios teams. My mother wouldn't let me play hockey, and the Blackhawks weren't on TV much, eventually due to the (now infamous) Bill Wirtz theory that TV broadcasts reduced paid attendance, so I didn't have too much exposure to the league as a whole as a kid.
I moved to NY for college in 1995. The city was still abuzz with the spillover from the '94 Stanley Cup team, and one of my new college buddies was a huge fan, having grown up in New Jersey. We started watching games at the bar on a regular basis. Since he was a big fan and the Rangers were always on (compared to the Devils or Islanders, at least in Manhattan, and especially compared to the Blackhawks), I got to know the roster and started to feel like it was "my" team.
When I started working in Manhattan after college, this same friend and I went in on a partial season with some of his other friends (we got something like 6 games a year). MSG was extremely convenient, and the atmosphere, even with those horrid teams post-Gretzky, was great for a young guy in the city. I put in for season tickets (there was a waiting list back then) and was able to get full-season tickets in 2002.
Since then, I've only become more involved, following the ins-and-outs of the NHL on blogs and forums like this one and becoming immersed in Rangers nation. I started playing hockey myself as an adult several years ago, and that further strengthened my bonds with fellow fans.
Today, I strongly identify with the Rangers as my team, and no all the details on the roster, prospects and the draft. Though I still root for the Blackhawks out west, the Rangers are my hometown team now, after nearly 20 years here. With my own children growing up here, I hope they will soon be able to answer this question much more simply, as several others have, with "born in to it".