I'd say that every team has their own rivalry going with another team somewhere. It's certainly not anything like college or pro rivalries, or even high school rivalries, but I think everyone has got a team or two that they face at a local regional and strive to do better than.
Karthik, being mentioned, he also had a pretty good 2056-1114
history speech at GTRWest last year.
There's also a friendly rivalry between the teams down in Texas, particularly 118 and 148, though that might just be an off the field prank rivalry...(Who says 148 is all serious and no fun?
)