Robb Nen. Nen saved 108 games for the Marlins between 1994-1997.
Trevor Hoffman with 601. Mariano Rivera is the all-time saves leader.
Bob Stanley, who pitched with the Red Sox between 1977-1989, is the Red Sox career saves leader with 132. Through games played on June 13, 2009 Jonathan Papelbon has 129 career saves and, barring disaster, will take over as Red Sox career saves leader shortly.
I couldn't find a rookie Marlins that played for the Phillies that has the record for most saves as a rookie. However, Dontrelle Willis in his rookie season had 14 wins, a Marlins team record for a rookie. He is currently on the Phillies.
Fingers had 341 saves in his MLB career.
John Franco. Franco had 424 career saves which is 4th most in MLB history. He led the National League in saves in 3 seasons (1988, 1990, 1994) but was never the MLB season leader.
Mariano Rivera with 230 saves.
Through the 2010 postseason, Mariano Rivera has the most saves, with 42.
In 1996, Miguel Batista pitched in 9 games for the Florida Marlins, with an ERA of 5.56. He started 0 games and finished 4, pitching no complete games. He threw no shutouts and recorded no saves, ending up with 0 wins and 0 losses. He pitched a total of 34 outs, facing 49 batters. He gave up 9 hits and 7 earned runs, but no home runs. He struck out 6 batters and walked 7.
In 2005, Yorman Bazardo pitched in 1 game for the Florida Marlins, with an ERA of 21.6. He started 0 games and finished 0, pitching no complete games. He threw no shutouts and recorded no saves, ending up with 0 wins and 0 losses. He pitched a total of 5 outs, facing 12 batters. He gave up 5 hits and 4 earned runs, but no home runs. He struck out 2 batters and walked 2.
In 1999, Reid Cornelius pitched in 5 games for the Florida Marlins, with an ERA of 3.26. He started 2 games and finished 0, pitching no complete games. He threw no shutouts and recorded no saves, ending up with 1 win and 0 losses. He pitched a total of 58 outs, facing 76 batters. He gave up 16 hits and 7 earned runs, but no home runs. He struck out 12 batters and walked 5.
In 2003, Toby Borland pitched in 7 games for the Florida Marlins, with an ERA of 1.86. He started 0 games and finished 1, pitching no complete games. He threw no shutouts and recorded no saves, ending up with 0 wins and 0 losses. He pitched a total of 29 outs, facing 40 batters. He gave up 3 hits and 2 earned runs, but no home runs. He struck out 4 batters and walked 8.
In 2010, Jay Buente pitched in 8 games for the Florida Marlins, with an ERA of 6.55. He started 0 games and finished 2, pitching no complete games. He threw no shutouts and recorded no saves, ending up with 0 wins and 0 losses. He pitched a total of 33 outs, facing 59 batters. He gave up 16 hits and 8 earned runs, but no home runs. He struck out 9 batters and walked 11.