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. Johnny Bench (1967-83, Reds) WAR 78.1 OPS+ 126 PA 8674 (WAR/PA .0090) MVPQ: 72, 74
2. Gary Carter (1974-92, Expos) WAR 72.9 OPS+ 115 PA 9019 (.0081) MVPQ: 87
3. Pudge Rodriguez (1991-2011, Rangers) WAR 82 OPS+ 106 PA 10270 (.0080)
4. Bill Dickey (1928-46, Yankees) WAR 62.95 OPS+ 127 PA 7065 (89) MVPQ: 30
5. Gabby Hartnett (1922-41, Cubs) WAR 62.75 OPS+ 126 PA 7297 (86)
6. Carlton Fisk (1969-93, Red Sox) WAR 71.55 OPS+ 117 PA 9853 (73)
7. Mike Piazza (1992-2007, Dodgers) WAR 61.55 OPS+ 142 PA 7745 (79) MVPQ: 97
8. Yogi Berra (1946-65, Yankees) WAR 64.35 OPS+ 125 PA 8359 (77)
9. Buck Ewing (1880-97, Giants) WAR 58.85 OPS+ 129 PA 5772 (102)
10. Mickey Cochrane (1925-37, Athletics) WAR 53.9 OPS+ 129 PA 6207 (87)
11. Joe Mauer (2004-, Twins) WAR 59.8 OPS+ 126 PA 7417 (81) MVPQ: 09
12. Gene Tenace (1969-83, A's) WAR 47.95 OPS+ 136 PA 5527 (87)
13. Joe Torre (1960-77, Braves) WAR 56.85 OPS+ 129 PA 8802 (65)
14. King Kelly (1878-93, White Stockings) WAR 54.7 OPS+ 139 PA 6457 (85) MVPQ: 86
15. Jorge Posada (1995-11, Yankees) WAR 54.2 OPS+ 121 PA 7150 (76)
16. Brian Downing (1973-91, Angels) WAR 53.5 OPS+ 122 PA 9309 (57)
17. Ted Simmons (1968-88, Cardinals) WAR 52.35 OPS+ 118 PA 9685 (54)
18. Buster Posey (2009- Giants) WAR 42.1 OPS+ 135 PA 4260 (99)
19. Thurman Munson (1969-79, Yankees) WAR 46.25 OPS+ 116 PA 5905 (78)
20. Charlie Bennett (1878-93, Wolverines) WAR 45.2 OPS+ 119 PA 4310 (105)
21. Russell Martin (2006 – Dodgers) WAR 44.3 OPS+ 102 PA 6047 (73)
22. Yadier Molina (2004- Cardinals) WAR 47.95 OPS+ 98 PA 6700 (72)
23. Darrell Porter (1971-87, Royals) WAR 44.25 OPS+ 113 PA 6570 (67) MVPQ: 79
24. Ernie Lombardi (1923-39, Reds) WAR 40.05 OPS+ 126 PA 6352 (63)
25. Roy Campanella (1948-57, Dodgers) WAR 38.85 OPS+ 123 PA 4815 (81)
(last out - Victor Martinez)