Florida State & Florida and Florida State & Miami are two pretty intense rivalries. The Gators have rebuilt while Miami and FSU are rebuilding. In the next few years, all Hell will break loose on Florida Gridirons. Oklahoma & Texas is a very heated rivalry, as well as Oklahoma & Nebraska (down but not out).
Florida State-Miami has been a great rivalry. Both teams have been on a downswing, but the rivalry is still a good one and will get better again as they get better.
Back in the glory days of Florida-Miami (Florida Flop, ornage fights, etc) the trophy was a Seminole Indian canoe that had been made by the Seminole tribe several decades ago.