#1 PAC-10, #2 Big-10
None. Since the expansion to 16 teams.
00000000 go big red
The Oklahoma Sooners have won eight Big 12 Conference championships, in 2000,2002,2004,2006,2007,2008,2010, and 2012 (with Kansas State.)
Penn State won national championships in 1982 and 1986. They were the Big 10 champions in 1994 and co-champions in 2005.
As of the start of the 2007 season, Oklahoma has won 5 Big 12 South Division championships and 4 overall Big 12 championships. Prior to the formation of the Big 12, Oklahoma played in the Big Eight Conference. Oklahoma won, or shared in winning, 32 Big Eight conference titles.
Virginia Tech hasn't won any National Championships in football. They have made one appearance, losing to Florida State in 2000 (Virginia Tech was still a part of the Big East at this time).
From 1912, which is when Ohio State joined the Big Ten, they have won 32 Big Ten Championships.
The Wisconsin Badgers Men's Basketball team has a total of 19 Big Ten Championships. (17 Regular Season Championships, two Conference Tournament Championships)
1 - Ohio State ten years ago versus Miami
a big zero
Oklahoma has won 31 big 12 championships. I'm not sure of the breakdown by sport, however.
Nebraska won 29 Big 8 championships (24 outright and 5 as co-champion) and, prior to the 2010 championship game that Nebraska will play in, 2 Big 12 championships.
19 total championships