I guess we could break them up into 2 categories, depending on the helmetness of your school:
1 - non-NC teams
2 - didn't win the conference, but were still cool/awesome/different/unique/noteworthy/sentimental
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Here, I'll start.
I really liked those mid-90s North Carolina teams, with the great defenses. But they never got over the FSU hump.
The 97 Gators - were #1 for a few weeks, but wound up being underdogs by the end. Only Spurrier team to lose to UGA, but spoiled FSU's natty. I played HS ball with the QB, and RB Fred Taylor and WR Jacquez Green finally got to be "the guy" at their positions and put up gaudy numbers. Didn't even win the east, but wound up #4 in the country.
1999 Georgia Tech, especially QB Joe Hamiton. He was small, but could do anything. He was like a video game. And the Tech offense that year was innovative - incorporating more than a little option with a lot of passing. They had a great game vs #1 FSU early and lost too many games down the stretch, but they were entertaining.
1990 Gators - Spurrier's first year, ineligible for anything. Into the first game, it was like "oh, okay, so we're going to throw the ball 400 times this year". It was just fun, all the big plays. Spurrier luckily inherited a salty defense, so 90 and 91 were legit teams.