The ND dynamic is interesting, as a lot of teams consider them to be their rival, but it's not really reciprocated other than with USC for the most part.
Teams like OSU and Texas have a similar, albeit much lesser phenomenon within their conferences, where everyone circles that game on their calendar if it's scheduled. In some cases it gets real similar to the ND phenomenon, like the dynamic between Penn State and OSU.
SEC teams probably have the most "rivals," as many have one in-state OOC on the annual at the end of the season, along with their conference rival(s). Hell, Florida had two OOC rivals at one point.