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What's the best team you can remember that didn't win anything of consequence.  No division or conference title, no NC, none of that.  But they were good - damn good. 

For Florida, it's either the '84 team that started the year with a loss and tie before finishing 9-1-1 and SEC champs, only for that to be voted away a month later.  An on probation so not even a bowl win.  Was likely the best team in the country that year.

The other is the 2001 team.  Lost twice - missing the starting RB in both games, Grossman at QB (who probably should have won the Heisman).  Best Spurrier offense since Wuerffel (and perhaps better). 
Didn't win the division, but probably would have posed the greatest challenge to the '01 Miami juggernaut.

2006 for Michigan. 2016 and 2018 to a lesser extent, too.

1983 Texas, awesome dominating defense and pretty good offense, in line to win the NC that year, and somehow managed to lose a bowl game to a middlin' team that caught a late lucky break or two.

The late, great Hooky Hornstein/Charley Horse often lamented that loss to Georgia in the Cotton Bowl.
But, still, Texas did win the SWC that year.  That was reasonably important.

I'll go with a weird one.

2002 Penn State.

They lost to Iowa in OT in a poorly officiated game.  A complete pass in OT was called incomplete by an official.  Iowa would go undefeated in the B1G that year.

They lost to Michigan away in OT in another poorly officiated game.  Late in the fourth, Penn State completed a pass to Tony Johnson in which he got both feet in bounds, but the officials called it incomplete.  This play would have put Penn State in FG range for the game winning score.  Michigan would finish the season ranked #9 in the country.

They lost to Ohio State away by a score of 7-13.  Ohio State completed a LONG 3rd down pass in which the ball hit the turf nearly 3 yards in front of the receiver, and bounced into his hands.  Called complete by the official.  This allowed OSU to run more time and hit a field goal, not to mention the flip in field position.  On the preceding series, a long pass to Bryant Johnson was foiled by blatant pass interference.  Chris Gamble (OSU), the interfering player making his first start on defense, said afterwards, "I tapped him a little early and was relieved when there was no flag."  Ohio State would go undefeated in the B1G and win the national championship.

This season changed Paterno's view on instant replay and it was implemented by the B1G two years later.

They also lost to Auburn in their bowl game by a score of 9-13.  Auburn scored a TD with 2:13 left in the game to take the lead for good.

A season in which Penn State caught every bad break there was. 

2015 Ohio State

2015 Ohio State

2015 won a share of the B1G East Title, which renders them ineligible for this exercise. 

For Michigan it’s probably 2016. That defense was a good as I’ve seen at Michigan in some time.

Wilton Speight breaking his shoulder at Iowa and losing by 1 point on a last second FG really changed the trajectory of that team. They were just beating the snot out of everyone up until that point. Speight was never the same since that injury either, he continually got worse year after year. 

They could’ve made up for it in Columbus but they shit the bed up double digits and fell apart and lost by 3 in OT. 

If Speight doesn’t suffer that injury they might not have lost to Iowa or Ohio State.