Obviously, the answer is whatever conference your team plays in. And noone is gonna convince anyone else here otherwise. Let me try to give a somewhat objective opinion:
Of all the major conferences:
Football: ESPN started their championship presented to the best football conference this year, specifically to address this issue. This went to the Big Ten. This is not because they are overated, sucky or anything else I saw in the other thread. This is because they beat teams in other conferences in their respective biggest games of the year, including taking match-ups with the Big12, Big East, two matchups with the SEC, and another with the Pac-10. Last time I looked, they also had the team that won a national championship.
Baseball: Warm weather conferences only need apply. (Though Ohio State fielded a very nice team this year). Give it to the Big-12, Texas, Baylor, etc. SEC is a close second.
Hockey: Of the major conferences? Tough to decide, but that Minnesota team is always amazing.
Basketball: The ACC for right now. I'm not so sure in 2004, cause they just diluted the strength by adding shaky basketball programs.
Wrestling: I really have no clue. But the best ones always seem to come from Iowa and the Big Ten.
Fencing: Let's go with the Ivy League here.
Women's Sports: Pac-10 for things like swimming, diving, some soccer, certainly softball, etc. Big East or SEC for basketball. ACC women play some mean soccer.