Steve Worster's three years on the varsity team represent the pinnacle of Texas Longhorn football. The Horns went 30-2-1 overall and 3-0 vs. OU, winning the natty outright in '69 and gaining the UPI championship (pre-bowls) in '70. That has to be the Horns' best-ever 3-year run. (Looking it up, I find that the '62-'64 run had the same record--overall and against OU.)
Since then, one NC and a 29-20-3 record vs. OU.