The only player worth discussing as a Hall of Fame candidate is Bernie Williams.
WilliamsAt his peak, Williams was a terrific offensive force, even though he reached 30 home runs just once in his career. From 1995 through 2002, he averaged .321/.406/.531 with 105 runs and 102 RBIs per season. He won four Gold Gloves, despite his weak throwing arm; the defensive metrics never matched his reputation and Baseball-Reference.com grades out Williams as a below-average center fielder over his career. He sure seemed smooth and effective out there, however. It's an extremely strong peak, punctuated by starring on four World Series champions, arguably the most valuable player on those teams. (From 1996 through 2002, Derek Jeter had 35.1 WAR according to B-R, Williams 34.6, Andy Pettitte 27.3 and Mariano Rivera 24.3.)
Williams had seven seasons with an OPS+ of 130 or higher -- OK, that's a lot fewer than the all-time great center fielders like Willie Mays and Mickey Mantle -- but it's the same total as Hall of Fame center fielders Duke Snider and Earl Averill, the same number as Andre Dawson (who had seven such seasons, but three as a right fielder), and more than Larry Doby and Kirby Puckett. Williams had nine seasons with 3+ WAR as a center fielder -- the same number as Snider and Richie Ashburn, more than Hall of Famers Max Carey, Edd Roush, Dawson (eight in his career, seven as a center fielder) or Puckett.
All that certainly puts Williams in the discussion with the bottom rung of Hall of Fame center fielders. What he lacks, of course, is the career longevity. His first quality season didn't come until he was 25, and that came in 1994, the strike season. After hitting .333 in 2002 at age 33, he suddenly declined, and hit just .263 with 61 home runs over his final four seasons. So while a guy like Dawson managed to rack up counting stats (1591 RBIs, 2774 hits, 1373 runs) with some mediocre seasons, Williams' career essentially consists of his peak and not much else (1257 RBIs, 2336 hits, 1366 runs).
I always thought Williams was the unappreciated star on those Yankee teams. He's on the cusp, but he falls a little short of Hall of Fame status in my book, and the reality is he'll receive very little support from the voters, who historically favor longevity over peak value.
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Part of the problem for any marginal candidate like Williams -- there are too many qualified candidates to choose from. The backlash against steroid-era players has created a crowded ballot, and voters are limited to a maximum of 10 players. On this ballot alone, the following players all of have some sort of Hall of Fame case (not saying they all deserve it, just that they deserve serious consideration): Jeff Bagwell, Barry Larkin, Edgar Martinez, Don Mattingly, Fred McGriff, Mark McGwire, Jack Morris, Dale Murphy, Rafael Palmeiro, Tim Raines, Lee Smith (cough), Alan Trammell, Larry Walker and Williams. That's 14 names.