Well the 2001 World Series is definately my favorite championship. Yes I am in Arizona and I have been a Diamondbacks fan since their first game (which I was there). Also I have never liked the Yankees. I still get goose bumps every time I see the replay of Luis Gonzalez hitting the game winning single and him jumping up and down. That was great. Before that I grew up a Cincinnati Reds fan and the 1990 World Series was pretty great too. Sweeping the Bash Brothers (Mark McGwire and Jose Canseco) and the rest of the Oakland A's when being such huge underdogs was impressive.
As far as rivalries go, so many to chose from the old Lakers and Celtics of the 80s had some good series.