The longest winning streaks (consecutive games) in baseball are as follows:

1880 Chicago White Stockings(Cubs) 20 won / 0 Tied / 11 at home
1884 St. Louis Maroons 20 Won / 0 Tied / 16 at home
1884 Providence Grays 20 Won / 0 Tied / 18 at home
1916 New York Giants 26 Won / 1 Tied / 26 at home
1935 Chicago Cubs 20 won / 0 Tied / 18 at home
2002 Oakland Athletics 20 won / 0 Tied / 10 at home