.300, 100 Runs, 200 Hits, 50 Stolen Bases

.300, 100 Runs, 200 Hits, 50 SB: 2000-present

Ichiro Suzuki (Mariners) 2001: .350, 127 R, 242 H, 56 SB

Juan Pierre (Marlins) 2003: .305, 100, 204, 65

Hanley Ramirez (Marlins) 2007: .332, 125, 212, 51

Carl Crawford (Rays) 2009 (?) .316, 71, 137, 52

(Projected: .316, 105, 201, 77)

Just Barely Missed:

Juan Pierre (Marlins) 2004: .326, 100, 221, 45

Jose Reyes (Mets) 2006: .300, 122, 194, 64

Jose Reyes (Mets) 2008: .297, 113, 204, 56

For comparison:
Ty Cobb 6 (1909, 1911-12, 1915-17)
Lou Brock: 2 (1970, 1971)
Craig Biggio: 1 (1998)
Kenny Lofton 1 (1996)
Tony Gwynn 1 (1987)
Willie Wilson 1 (1980)
Tim Raines: 0
Rickey Henderson: 0
Joe Morgan: 0