The most home runs hit in a single season was by Barry Bonds in 2001. In his 2001 season, Bonds hit 73 homeruns beating Mark McGwire's previous record of 70.
source: hallofshoes.com
The highest batting average in a single season was recorded by Nap Lajoie. In his 1901 season with the Philidelphia Athletics, Lajoie hit an astounding .426.
Pitching Records
The most strikeouts in a single season were thrown in 1886 by Matt Kilroy. Kilroy struck out 513 batters that year.