1999 Las Vegas Bowl - Fresno State
2001 Las Vegas Bowl - USC
2003 Liberty Bowl - Southern Miss
2004 Fiesta Bowl - Pittsburgh
2005 Emerald Bowl - Georgia Tech
2006 Armed Forces Bowl - Tulsa
2007 Poinsettia Bowl - Navy
Just to note, I do not believe Utah has ever played an SEC team in a bowl game.
To add to GreatDanish's post:
99 Las Vegas Bowl - Utah 17, Fresno St. 16
01 Las Vegas Bowl - Utah 10, Southern Cal. 6
03 Liberty Bowl - Utah 17, So. Miss 0
04 Fiesta Bowl - Utah 35, Pitt. 7
05 Emerald Bowl - Utah 38, Georgia Tech. 10
06 Armed Forces - Utah 25, Tulsa 13
07 Poinsettia Bowl - Utah 35, Navy 32
Obviously, they have a habit of winning bowl games. There are a couple of opponents that are well respected. In the 2001 Las Vegas Bowl, they held Southern Cal to only one yard rushing.
Overall though, their bowl opponents are not SEC caliber teams. Not so sure that means very much as every team has to reinvent itself annually. We can attest to that.