“Rivals” seems to be defined in different ways, but from my perspective, I am defining a rival as a team that stirs deep passions of dislike/hatred for the team you are playing. In my mind that passion is keyed by consistency, so I don’t include teams who may have lots of wins against us but many of those may be prior to us entering into our program’s real success starting in the 80’s and beyond. Anyone who has been to a home game at the Orange Bowl or Hard Rock immediately knows there is a completely different level of noise that is unexplainable when we are playing a true rival.
On the rival side:
UF and FSU - we battle them for state recruiting and there is a long history with both. When we are up, they are usually down and vice versa, so they are the most important of the rivals.
Notre Dame - I attended school from ‘87-’90 and anyone there during that time understands the dislike/hatred to this day. Jimmy demoralized Faust and from then, it was game on. No one liked us knocking them off their pedestal, so every game was bloodsport, and while they believe we split an important four game set, the entire world knows Cleveland Gary fumbling was one of the most obvious bad calls, next to Ohio State’s pass interference phantom call, that cost us two national titles that rightfully should be ours. That unfairness will never sit well with most Miami fans.
Ohio State - for the same reason that many have already mentioned, the fact that they possess a title trophy that rightfully should be stored in our case, will always make me want to kick their asses. We don’t play them often, but the bigger connection is recruiting. Their fake title led them to two decades of dominance, which was aided by our two decades of failure. They weren't the reason for our failure, but they benefited from it. So many of their key playmakers that led to their success was plucking those players from Florida. If we go up, I believe they will go down.
Virginia Tech and North Carolina - I believe these are current, but can be temporary rivals IF we return to winning. We used to dominate both teams and they weren’t even on our radar screen, but they have both capitalized on our misfortune over the last two decades. They are both a function of recency bias and their success against us. That success has turned both of their fanbases into a group of obnoxious wanna-be champions with no trophies in their case. UNC, for what Rellyrell already mentioned, raises passions because they have not only beaten us, but have been completely disrespectful about it, not only with the most smug piece of garbage coach who wants to try and disrespect us in every way, but is accompanied by an obnoxious fan base who somehow think their football history deserves the same respect their basketball program has. Well, their about to find out where their rightful place as a football program will be in the coming years ahead as well.
Non-rivals:
Penn State - Times they’ve beaten us have been won without controversy, but from the ‘80s on, outside of a title game we should have won in ‘85, we have usually had the last laugh with them.
Clemson - Dabo is another smug piece of garbage that will have his day in court with us, but I take him off the list because of one key reason, he got Golden fired. Clemson's 15 minutes of fame may have just expired, since Dabo refuses to adapt to today's game.
Georgia Tech, Pittsburgh, BC, West Virginia, Nebraska - I could be wrong, but since the ‘80s, I don’t think any of them have had any consistent success against us, so they don’t really drive the passions with me.
UCF, USF, FIU - they aren’t even on the radar, as them having random success while we have sucked wouldn’t stir those passions with me, as I don’t see them on the same level. That goes with any team that may have beaten us during a time when we were not a good football program, but that was more a function of us being bad, rather than them being good.