For years, mine was Dallas -- I love Dirk, and I loved their style of play under Avery. I always played as them in video games, because of backcourt speed (Harris, Terry, and Mo Ager was inexplicably awesome in 2K8), alternating bigs who could just get boards, and scoring from Dirk and a little of everything from Howard.
Since the Kidd trade, I got disgusted with them, because I can't stand Kidd.
Now I find myself drawn to the Nets. I still love Devin Harris (and Mo), plus Yi is really intriguing to me. Now they've added this Anderson kid from Cal, who looks like a player, and CDR. Vince is detestable, but he'll be dealt either this year or next.
Outside of players, they've got a fun roster to think about, plenty of cap space/future thinking to allow for all kinds of trade speculation. Throw in the Brooklyn/Jay-Z aspect, and I just really enjoy them, almost as a concept.
Anyway, who do you find yourself rooting for when the Celts aren't on?