Bay, Los Angeles Angels right-handed starter John Lackey and St. Louis left fielder Matt Holliday were the marquee players filing on the first day. All three are testing the free-agent market for the first time in their careers.
Lackey has spent his entire eight-year career with the Angels, while Holliday spent time with Colorado and Oakland before joining the Cardinals, and Bay was with San Diego and Pittsburgh before going to the Red Sox.
Bay, 31, the 2004 National League Rookie of the Year and .280 career hitter, hit .267 with career-highs in homers (36) and RBI (119) last season.
Lackey has won at least 10 games each season.
Holliday, the 2007 runner-up in National League MVP voting, has a .318 batting average with 152 homers and 592 RBI.