Toledo - BG's biggest rival, a mere 20 minutes north up I-75. There have been times when their students have come down to BG to paint their logos and colors on our rock (which is annoying, but it is a spirit rock and I can let it slide as part of the rivalry), but the time a few Rocket fans came down and spray painted "F*** BG" and other similar messages on sidewalks and a few University signs... that sealed my hatred.
Ohio State - I grew up as a non-Buckeye fan in Ohio, and it's always been ridiculous watching the way their fans worship this team and act like every other team is beneath them. Now, I have some friends who just happen to be Buckeye fans and are perfectly reasonable people who don't have the snobby attitude about their team, but as a general rule, Buckeye fans are some of the worst fans in college football. Their insistence upon being called "THE Ohio State University" is perhaps one of the best examples of this.
Florida - I'll admit first off that even though I know I'm supposed to hate everything associated with this program, I still kinda like Urban (leftover from his days at BG, and because even though he's at the helm of our rival, I still think he's a pretty talented coach.) But as for the rest of the program, I wouldn't be a Tennessee fan if I didn't hate them.
Miami (OH) - Another rival of BG's. Some of my best friends went there, but I still can't stand the Redhawks. As the saying goes, Bowling Green is windy because Miami sucks and Toledo blows.
Alabama - Again, I feel like I would be remiss in my duties as a Tennessee fan if I didn't include them here.
Honorable Mentions:
Michigan - (Because around here, most people assume that if you're not an OSU fan, you're a Michigan fan.)
Western Kentucky - Half because of their status as being the other school located in a Bowling Green, (and because I somehow associate them with the misguided concept that BGSU is in KY), and also because of their reputation for taking cheap shots at our players' knees when they played us after they realized we had the game well in hand.