Lee Smith with 180 career saves with the Chicago Cubs (1980-1987).
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.
Fingers had 341 saves in his MLB career.
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.
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 2011, Sandy Rosario pitched in 4 games for the Florida Marlins, with an ERA of 2.45. 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 11 outs, facing 18 batters. He gave up 5 hits and 1 earned run, but no home runs. He struck out 2 batters and walked 2.
In 2009, Cody Ross pitched in 1 game for the Florida Marlins, with an ERA of 0. 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 3 outs, facing 4 batters. He gave up 1 hit and 0 earned runs, but no home runs. He struck out 0 batters and walked 0.
In 2001, Johnny Ruffin pitched in 3 games for the Florida Marlins, with an ERA of 4.91. 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 11 outs, facing 21 batters. He gave up 5 hits and 2 earned runs, but no home runs. He struck out 4 batters and walked 4.
In 2010, Brett Sinkbeil pitched in 3 games for the Florida Marlins, with an ERA of 13.5. 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 6 outs, facing 13 batters. He gave up 2 hits and 3 earned runs, but no home runs. He struck out 1 batter and walked 5.
In 2010, Scott Strickland pitched in 3 games for the Florida Marlins, with an ERA of 9. 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 6 outs, facing 11 batters. He gave up 5 hits and 2 earned runs, but no home runs. He struck out 0 batters and walked 1.