- 2× NBA champion (1994, 1995)
- 2× NBA Finals MVP (1994, 1995)
- NBA Most Valuable Player (1994)
- 12× NBA All-Star (1985–1990, 1992–1997)
- 6× All-NBA First Team (1987–1989, 1993, 1994, 1997)
- 3× All-NBA Second Team (1986, 1990, 1996)
- 3× All-NBA Third Team (1991, 1995, 1999)
- 2× NBA Defensive Player of the Year (1993, 1994)
- 5× NBA All-Defensive First Team (1987, 1988, 1990, 1993, 1994)
- 4× NBA All-Defensive Second Team (1985, 1991, 1996, 1997)
- NBA All-Rookie First Team (1985)
- IBM Award (1993)
- 2× NBA rebounding leader (1989, 1990)
- 3× NBA blocks leader (1990, 1991, 1993)
- No. 34 retired by Houston Rockets
- NBA anniversary team (50th, 75th)
- NCAA Final Four Most Outstanding Player (1983)
- Consensus first-team All-American (1984)
- NCAA rebounding leader (1984)
- SWC Player of the Year (1984)
- No. 34 retired by Houston Cougars
- Houston Sports Hall of Fame (2018)
- Texas Sports Hall of Fame (1998)
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