Florida and Georgia
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UNC vs Duke in Basketball. Duke students tent outside of the ticket gate for multiple days trying to get tickets, and no fans in any sports get more crazy than the Duke and UNC students at these games. They have played each other over 200 times, and due to the constant competitiveness of the two teams, each time they meet they are jockeying for a sport at the top of the ACC. Together, they have been to over 30 Final Fours!
It is a known fact that the Bear's/ Packer's rivalry is the fiercest rivalry in the NFL, but I'm not sure about all of sports.
No nba is one of the biggest sports in the world
auburn and Alabama
The NCAA oversees most U.S. college sports.
Glasgow Rangers -v- Glasgow Celtic, The Old firm Derby has been played 395 as of April 2011. Wiki it
me and me
The NCAA basketball tournament
The oldest rivalry in sports is between Liverpool and everton.
islanders vs. Rangers
OU Vs. Texas Red River Rivalry 4
There are 19 sports in men's and women's
The Steelers Biggest Rivalry is with the Cowboys as they matched up as two dominant teams of the 90s and faced off in the Superbowl at one point.