| 1984 | Named All-American by the American Association of College Baseball Coaches |
| 1984 | Sporting News College Player of the Year |
| 1987 | American League Rookie of the Year |
| 1987 | Sporting News Rookie of the Year |
| 1987-92, 1995-97 | American League All-Star team |
| 1990 | Rawlings Gold Glove Award, first base |
| 1992 | UPI Comeback Player of the Year |
| 1992, 1996, 1998 | Sporting News Silver Slugger team, first baseman |
| 1998 | Associated Press Player of the Year |
| 1998 | Baseball America's Major League Player of the Year |
| 1998-2000 | National League All-Star team |
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