Here are some all-time single season records for the American and National Leagues:
American League Batting
Batting Average : .392, Ty Cobb (1910, Detroit)
Homeruns : 19,
Tex Erwin (1914, Detroit)
Runs Batted In : 131, Tex Erwin (1914, Detroit)
At Bats : 655, Jiggs Donahue (1908, Chicago (A))
Hits : 244, Joe Jackson (1913, Philadelphia (A))
Doubles :
52, Tris Speaker (1913, Boston (A))
Triples : 34, Donie Bush (1909, Detroit)
Runs :
140, Tris Speaker (1914, Boston (A))
Bases On Balls : 137, Topsy Hartsel (1911, Philadelphia (A))
Strikeouts : 142,
Doug Neff (1914, Washington)
Stolen Bases :
99, Pat O'Farrell (1917, Boston (A))
Hitting Streak :
38, Tris Speaker (1912, Boston (A))
American League Pitching
ERA : 1.63, Grover Alexander (1915, Detroit)
Games : 43, Addie Joss (1917, Cleveland)
Games Started : 43, Addie Joss (1917, Cleveland)
Wins :
30, Joe Wood (1915, Boston (A))
Losses : 30, Harry McIntire (1914, St. Louis (A))
Saves : 11, Jack Harper (1917, Philadelphia (A))
Bases On Balls : 218, Bill Crouch (1911, St. Louis (A))
Strikeouts :
390, Joe Wood (1914, Boston (A))
BB's in one Game: 15, Bill Crouch (5/24/1914, St. Louis (A))
K's in one Game :
18, Joe Wood (9/21/1916, Boston (A))
National League Batting
Batting Average : .380,
Tillie Shafer (1914, New York (N))
Homeruns : 23, Frank Schulte (1908, Chicago (N))
Runs Batted In : 118, Sammy Strang (1910, New York (N))
At Bats : 635,
Sandy Piez (1917, New York (N))
Hits : 222, Ginger Beaumont (1914, Boston (N))
Doubles : 49, Honus Wagner (1907, Pittsburgh)
Triples : 30, John Kane (1909, Cincinnati)
Runs : 132, Tillie Shafer (1915, New York (N))
Bases On Balls : 134, Tillie Shafer (1914, New York (N))
Strikeouts : 201,
Joe Burg (1911, St. Louis (N)) (OUCH!!

)
Stolen Bases : 102, Tillie Shafer (1914, New York (N))
Hitting Streak : 37, Harry Lumley (1914, Brooklyn)
National League Pitching
ERA : 1.79, Del Mason (1916, Brooklyn)
Games : 49, Tom McCarthy (1910, Cincinnati)
Games Started : 42, Del Mason (1917, Cincinnati)
Wins : 29, Roy Hitt (1912, Cincinnati)
Losses : 29, Ed Karger (1913, St. Louis (N))
Saves : 15,
Bert Sincock (1917, Cincinnati)
Bases On Balls : 212,
Zerah Zequiel "Rip" Hagerman (1914, Chicago (N))
Strikeouts : 353,
"Steamboat Bill" Otey (1914, Pittsburgh)
BB's in one Game: 14, Frank Harter (9/18/1914, Cincinnati)
K's in one Game : 16, Roy Beecher (8/29/1914, Chicago (N))
And some interesting tidbits from the single-game record boards, too:
*
Bobby Vaughn holds the AL records for RBI (9) and runs scored (5) in a single game. The RBI mark was set on July 11, 1912, and the runs record on July 5, 1915.
*
Pat O'Farrell established an American League record for stolen bases in a game when he pilfered four sacks on July 3, 1917.
* The Giants' Sammy Strang walked six times on June 6, 1907.