The Bert Jones Colts in the mid to late '70s were annoying. That's the only rival I've severely disliked. Baltimore was easily our biggest rival in the '70s. But early in the decade we were on the upswing and they were old. It reversed in the mid '70s. Suddenly they had a ton of talent on both sides of the ball. It looked like we would be hard pressed to win the division for years.
Beyond anything, those Colts were simply lucky. Once they had a punt blocked for a late touchdown near the end of the year to lose a home game to the Lions. Dolphin fans were celebrating until it turned out the loss actually helped Baltimore in terms of playoff tiebreakers. Then there was the infamous Bert Jones non-fumble in a season finale against the Grogan Patriots. The referee blew the call and Baltimore rallied to win and clinch a playoff berth over the Dolphins. New England was essentially playing for Miami in that game, and darn did they give it a huge effort until that bogus call.
I hated the Patriots only in 2007 when they almost matched our signature achievement.
I'll always be convinced it must have been a rival who designed our stadium, and the current abomination of a logo. Those can't be friendly fire. Nobody is that inept.