The Kansas City Royals, Boston Red Sox and St. Louis Cardinals have so far made the most high-profile moves in exercising/declining team options for the 2016 season. Here's the full list of MLB teams and their transactions regarding players with team/mutual options for next year.
Arizona Diamondbacks
Exercised Brad Ziegler's $5.5 million team option
Exercised Josh Collmenter's $2 million mutual option
Atlanta Braves
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Baltimore Orioles
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Boston Red Sox
Exercised Clay Buchholz's $13 million team option
Chicago Cubs
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Chicago White Sox
Declined Alexei Ramirez's $10 million team option($1 million buyout)
Cincinnati Reds
Declined Burke Badenhop's $4 million team option ($1.5 million buyout)
Declined Skip Schumaker's $2.5 million team option ($500K buyout)
Cleveland Indians
Declined Ryan Raburn's $3 million team option ($100K buyout)
Colorado Rockies
Declined Justin Morneau's $9 million mutual option ($750K buyout)
Detroit Tigers
Declined Joe Nathan's $10 million team option ($1 million buyout)
Houston Astros
Declined Chad Qualls' $3.5 million team option ($250K buyout)
Kansas City Royals
Declined Alex Rios' $12.5 million mutual option ($1.5 million buyout)
Declined Jeremy Guthrie's $10 million mutual option ($3.2 million buyout)
Declined Jonny Gomes' $3 million team option
Exercised Wade Davis' $8 million team option
Exercised Alcides Escobar's $5.25 million team option
Los Angeles Angels
Declined David Murphy's $7 million team option ($500K buyout)
Los Angeles Dodgers
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Miami Marlins
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Milwaukee Brewers
Exercised Adam Lind's $8 million team option
Minnesota Twins
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New York Mets
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New York Yankees
Declined Andrew Bailey's $2 million team option
Oakland Athletics
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Philadelphia Phillies
Declined Cliff Lee's $27.5 million team option ($12.5 million buyout)
Pittsburgh Pirates
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San Diego Padres
Exercised Jaoquin Benoit's $7.5 million team option
Declined Clint Barmes' $2 million team option ($200K buyout)
Declined Corey Luebke's $7.5 million team option ($1.5 million buyout)
San Francisco Giants
Declined Nori Aoki's $5.5 million team option ($750K buyout)
Declined Marlon Byrd's $8 million team option (no buyout)
Seattle Mariners
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St. Louis Cardinals
Exercised Jaime Garcia's $11.5 million team option
Declined Jonathan Broxton's $9 million team option ($2 million buyout)
Tampa Bay Rays
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Texas Rangers
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Toronto Blue Jays
Exercised Jose Bautista's $14 million team option
Exercised R.A. Dickey's $12 million team option
Exercised Edwin Encarnacion's $10 million team option
Declined Maicer Izturis' $3 million team option ($1 million buyout)
Washington Nationals
Declined Casey Janssen's $7 million mutual option ($1.5 million buyout)
Declined Nate McLouth's $6.5 million team option ($750K buyout)