Atlanta Braves: The biggest former Arizona asset on the Braves is Chad Durbin, who had a very brief, bad tenure with Arizona in 2004 (7 games, 8.68 ERA), but has grown into a great reliever for Atlanta. Miguel Batista was traded from the Mets to Braves in August and made a few appearances. Lyle Overbay also signed with the Braves, but he was only a September player and not eligible for the postseason.
St. Louis Cardinals: No former Diamondbacks are currently with the Cardinals.
Baltimore Orioles: Arizona's own Joe Saunders gets the extremely crucial start today in the win-or-go-home wild card game. Bazooka Joe has a 3.63 ERA in 7 starts for the Orioles. Mark Reynolds is busy being Mark Reynolds: .221 average, 23 home runs, 159 strikeouts.
Texas Rangers: No former Diamondbacks are currently on the Rangers, either.
Reds: No former Diamondbacks.
Giants: Javier Lopez, who, like Durbin, had an awful time with Arizona, has been a good reliever for the Giants, posting a 2.50 ERA in 70 appearances. Xavier Nady signed with the Giants in September, so I don't think he's eligible for the post-season. Similarly, Yusmeiro Petit made one September start for them.
NLDS: Washington Nationals vs Wild Card Winner [October 7th, 12pm]
Nationals: Edwin Jackson, who threw a no-hitter for Arizona, started 32 games for the Nats with a 4.03 ERA. First baseman Adam LaRoche smacked 33 home runs this season, and Chad Tracy hit .269 as mainly a pinch hitter/defensive replacement. Zach Duke spent September in Washington and made 8 relief appearances.
ALDS: Oakland A's vs Detroit Tigers [October 6th, 3pm]
Oakland: Seriously, this franchise should be called the Athletibacks for all we've traded between each other. Stephen Drew is the most recent D'back to be involved in the trade. Jarrod Parker has been tagged to start Game 1, and Ryan Cook has been a solid reliever for them all year long, as had Jordan Norberto before he got hurt. Also injured over most of the summer, Colin Cowgill has been sparingly used as a defensive replacement in September, and I doubt he makes the post-season roster.
Detroit: Two big name pitchers are now with the Tigers: closer Jose Valverde and starter Max Scherzer. Papa Grande has saved 110 games in three seasons over there, though his ERA is closer to 4 than it should be. Scherzer, 16-7 with a 3.74 ERA, is scheduled to start Game 4 (if necessary).
ALDS: New York Yankees vs Wild Card Winner [October 7th, 3pm]
Yankees: No former Diamondbacks (whew!)