| 1989 | MLB-NL | Played in MLB All-Star Game (NL) | |
| 1992 | MLB-NL | NLCS Most Valuable Player | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |
| 1993 | MLB-NL | Played in MLB All-Star Game (NL) | |
| 1996 | MLB-NL | National League Cy Young Award | |
| | MLB-NL | NL MVP (Voting Rank: #11) | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |
| 1997 | MLB-NL | NL Silver Slugger Award (P) | |
| 1998 | MLB-NL | NL Cy Young Award (Voting Rank: #4) | |
| 2002 | Team | Atlanta Braves Player of the Year | |
| | MLB | Baseball America Second-Team Major League All-Star RP | |
| | MLB-NL | NL Cy Young Award (Voting Rank: #3) | |
| | MLB-NL | NL MVP (Voting Rank: #8) | |
| | MLB-NL | NL Rolaids Relief Pitcher of the Year | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |
| 2003 | MLB | Baseball America Second-Team Major League All-Star RP | |
| | MLB-NL | NL MVP (Voting Rank: #18) | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |
| 2004 | MLB-NL | NL MVP (Voting Rank: #21) | |
| 2005 | MLB-NL | Played in MLB All-Star Game (NL) | |
| | MLB | Roberto Clemente Award | |
| 2006 | Team | Atlanta Braves Player of the Year | |
| | MLB-NL | NL Cy Young Award (Voting Rank: # 7) | |
| 2007 | MLB | Branch Rickey Award | |
| | MLB-NL | NL Cy Young Award (Voting Rank: # 6) | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |