This is probably the most interesting topic I've read on this board. Plus, there have been some great answers given. For me, you have to look at key plays where UT, had they won the game, would've put them in position to win the conference or put them the national title hunt.
Someone mentioned the '92 Ark game. UT wins that game there is no way S. Carolina beats them. Bama only won 17-10 in Neyland and there would've been a re-match in B'ham.
Certainly the 4th down call at UF in '99. UT picks up the 1st down and goes on to win that game, they're back in New Orleans with a re-match against FSU.
2001, the Stallworth fumble sealed the deal against LSU. The squib kick against UGA had me screaming at the TV!
2004, the final play of the 1st half vs. ND. Sanders (or whoever called that play) should've been fired on the spot. Take a knee and go into halftime. Later that year, UT had Auburn on the ropes and played very undisciplined in the 2nd half of the SECCG.
2006, the pick 6 against UF as well as a couple of costly penalties cost UT the SEC title.
There are other plays mentioned that are heartbreaking as well. Thanks for the walk down misery lane!