One man's list; I tried to go with great players who are synonomous with that particular franchise, not just guys who passed through (like Sheffield or Josh Beckett with the Marlins, or most of the great players who made up the Blue Jays' World Series winners in the early 90s):
Yanks -- Babe Ruth
Red Sox -- Ted Williams
Orioles -- Brooks Robinson? Maybe Jim Palmer?Frank Robinson? Ripken? Murray? I'd go Frank.
Blue Jays -- Egads. Most of the great players from their World Series teams, like Molitor, Henderson and Winfield, were transients. Dave Stieb?
Rays -- None. Crawford
Twins -- Harmon Killebrew or Kirby Puckett.
Tigers -- Ty Cobb
Royals -- George Brett
White Sox -- Joe Jackson Pretty close, I might go Thomas
Indians -- Bob Feller
Rangers -- Nolan Ryan As a Ranger? Juan Gonzalez over Ryan. Maybe Pudge too. And Arod
Mariners -- Ken Griffey Jr. Arod?
Angels -- Tough one. Rod Carew, I suppose. Maybe Nolan Ryan again.
A's (Oakland era only) -- Reggie Jackson Canseco?
Phillies -- Mike Schmidt/Steve Carlton (tie) Schmidt
Mets -- Tom Seaver
Nats/Expos -- Gary Carter? Andre Dawson? Dawson
Marlins -- Haven't kept anyone great around long enough for consideration in this discussion.
Braves -- Hank Aaron
Brewers -- Robin Yount. Molitor was too much of a transient later in his career.
Cubs -- Gotta be Ernie Banks.
Astros -- Nolan Ryan, or Craig Biggio if you want a guy who played his whole career there.
Cardinals -- Stan Musial
Pirates -- Roberto Clemente
Reds -- Frank Robinson or Pete Rose
Rockies -- Todd Helton? Haven't had much else in 15 years, in terms of long-lived standouts.
Dodgers -- Jackie Robinson Koufax
Giants -- Willie Mays Bonds?
Padres -- Tony Gwynn
Diamondbacks -- Randy Johnson