Armando Benitez
Rafael Soriano with 45 saves for the 2010 Rays.
Susan Dunmire
The single season saves record in MLB is 57 (Bobby Thigpen) UPDATE: As of 9/18/08, Rodriguez has broken the MLB single season saves record with 59.
Armando Benitez holds the record for most saves in a singles season by a New York Met with 41, in 2001.
Through the 2008 season, that is Trevor Hoffman with 554.
Through the 2008 season, that is Ken Sanders of the 1971 Brewers who pitched in 83 games. He led the American League in saves that year with 31.
Kent Tekulve Mike Williams holds the Pirates team record for saves with 46 in 2002. Elroy Face holds the Pirates career save record with 188. Tekulve had 158 saves during his career with the Pirates.
On the last day of the 2010 season, Giants closer Brian Wilson tied the late Rod Beck's team record of 48 saves. Wilson was the 2010 major-league leader in saves.
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.
As of 9/19/2011: Mariano Rivera is the all-time saves leaders with 602. The single season record for saves is 62, held by Francisco Rodriguez.
Through the 2007 season, Trevor Hoffman of the San Diego Padres is the MLB all time saves leader with 524.
Trevor Hoffman