I've got each position carried out to 32 slots for a project that I don't believe fits this space, so I'll just include the top 25 here. I'll also include last player out. For some players, it's hard to slot them at a particular position (where does King Kelly go, for example) so I just chose one (if you don't see a first baseman in the top 25 who you know should be there, maybe he's a third baseman instead).
Each player is only listed with one team - the team that is most representative of his MLB performance. This is just merit, that's the only way I rank stuff - it's not social impact or the quality of their character. It's performance.
1. Willie Mays (1951-73, Giants) WAR 149.55 OPS+156 PA 12496 (WAR/PA .0120) EMVPQ: 64, 65, 63 MVPQ: 54, 62, 58, 60, 55, 66, 61, 57,
2. Ty Cobb (1905-28, Tigers) WAR 135.4 OPS+ 168 PA 13084 (.0103) EMVPQ: 17, MVPQ: 11, 10, 09, 15, 12,
3. Tris Speaker (1907-28, Indians) WAR 119.8 OPS+157 PA 11995 (.0100) MVPQ: 12, 14, 23, 16, 13
4. Mickey Mantle (1951-68, Yankees) WAR 100.15 OPS+172 PA 9907 (101) EMVPQ: 57, 56 MVPQ: 61,
5. Joe DiMaggio (1936-51, Yankees) WAR 76.7 OPS+155 PA 7672 (100) MVPQ: 37, 41, 39,
6. Ken Griffey (1989-2010, Mariners) WAR 87.9 OPS+ 136 PA 11304 (78) MVPQ: 96, 97, 93
7. Jim Edmonds (1993-2010, Cardinals) WAR 64.9 OPS+132 PA 7980 (81)
8. Carlos Beltran (1998-17, Mets) WAR 73.7, OPS+119 PA 11031 (67) MVPQ: 06,
9. Mike Trout (2011- Angels) WAR 55 OPS+ 172 PA 4065 (135) EMVPQ: 12 MVPQ: 16, 13, 15, 14
10. Billy Hamilton (1888-1901, Phillies) WAR 61.65 OPS+ 141 PA 7608 (81) MVPQ: 94
11. Reggie Smith (1966-82, Red Sox) WAR 60.1 OPS+137 PA 8051 (75)
12. Duke Snider (1947-64, Dodgers) WAR 57.55 OPS+140 PA 8237 (70)
13. Jimmy Wynn (1963-77, Astros) WAR 58.15 OPS+129 PA 8011 (73) MVPQ: 65,
14. Chet Lemon (1975-90, Tigers) WAR 57 OPS+121 PA 7874 (72)
15. Richie Ashburn (1948-62, Phillies) WAR 64.65 OPS+ 111 PA 9736 (66) MVPQ: 58,
16. Andre Dawson (1976-96, Expos) WAR 63.75 OPS+119 PA 10769 (59) MVPQ: 81
17. Kirby Puckett (1984-95, Twins) WAR 53.7 OPS+124 PA 7831 (69)
18. Andruw Jones (1996-2012, Braves) WAR 58.7 OPS+111 PA 8664 (68)
.
19. Kenny Lofton (1991-2007, Indians) WAR 61.15 OPS+107 PA 9235 (66)
20. Fred Lynn (1974-90, Red Sox) 51.1 OPS+ 129 PA 7923 (64) MVPQ: 79
21. Bernie Williams (1991-06, Yankees) 58.15 OPS+ 125 9053 (64)
22. Cesar Cedeno (1970-86, Astros) WAR 50.05 OPS+123 PA 8133 (62)
23. Torii Hunter (1997-15, Twins) 53.7 OPS+ 110 PA 9692 (55)
24. Johnny Damon (1995-12, Royals) 54.5 OPS+ 104 PA 10917 (50)
25. Lenny Dykstra (1985-96, Phillies) 43.85 OPS+ 120 PA 5282 (83) MVPQ: 90
(last out - Andrew McCutchen)