I love that so many replies list UCONN first. Other teams be damned!
In all seriousness, the three pro teams I follow the most intensely are the Red Sox, Nets, and Patriots. The Sox are an interesting story - it was actually the 2003 ALCS that made me fall in love with the team. In my twisted 2nd-grade mind, there was something beautiful about a community of fans sharing that much heartbreak, and I wanted to be a part of that camaraderie. Then I got lucky...Nets happened shortly thereafter I was a huge Jason Kidd fan growing up, and when Vince Carter came along there was actually some solid ball being played in the Meadowlands.
I also cheer for the Canadiens and Liverpool FC, but I don't follow either sport with as much attention.