Next up would be Jason Varitek.
Varitek was a pretty good catcher. He played 15 years, all for the Red Sox. I say he played 15 years, but the first of those he played just 1 game, but still. He hit .256/.341/.435 with 193 home runs. He made 3 All-Star teams, had 1 Gold Glove, 1 Silver Slugger and got MVP votes 3 times (highest finish was 21st).
And, he was 'captain' of the Red Sox. He played in 63 playoff games, hitting .237/.292/.452 with 11 home runs. He has 2 World Series rings.
He got all the character, leadership, toughness, gamer, teammate, winner, grit accolades from TV commentators. Kind of a Jeter-lite.
But I don't see him as a Hall of Famer, though I'm sure he will get some votes from the BBWAA.
Billy Wagner is the 3rd of the closers on the this year's Hall of Fame ballot (Lee Smith and Trevor Hoffman are the others). It is his second time on the ballot. He was on 10.5% of the ballots last year.
He pitched for 5 different teams, in his 16 year career, spending most of it with the Houston Astros.
Wagner sits 6th on the all-time saves list (Francisco Rodriguz passed him this year) (the other two on the ballot Trevor Hoffman and Lee Smith, are 2nd and 3rd on the career list). He made 7 All-Star teams, won 1 reliever of the year award, got MVP votes twice and Cy Young votes twice.
He pitched in 853 games, had a 2.31 ERA (terrific career number) with 422 saves. He averaged 11.9 strikeouts per 9 innings (that's a pretty amazing career number).
Billy pitched in the playoffs 7 times, but never made it to the World Series. He has pretty terrible numbers in 14 playoff games.
Matt W's chart:
A lot of debate about the Hall of Fame relates to comparing a candidate against others elected and excluded. The chart below shows pitchers who played the majority of their career after 1945 (excluding active players, and those on the ballot or yet to hit the ballot) according to how long they played (innings pitched) and how productive they were (adjusted ERA). This is not meant to be definitive, but a high level starting point showing how players with similarly productive and lasting careers have fared.
Similar Players: None, really. Mariano Rivera (1283 innings, 49 ERA-) would be the closest, but that's 400 more innings + playoffs. Tom Henke is the closest on there, and he was one-and-done with 1.2% support.