How many types of two dollar bills are there?

Depending on how you define "type", there have been at least 15 major varieties of US $2 bills since the denomination was first printed in 1862. Within those varieties there have been other more minor changes resulting in more than 2 dozen differences.

Before all bills were standardized in 1928, $2 bills were printed as United States Notes, Silver Certificates, Treasury Notes, and National Currency Notes. Several of those series had multiple designs.

Starting in 1928, all $2 bills were printed as United States Notes with red seals. Bills were further standardized in 1953, and $2 bills were again redesigned. The 1963 issue was modified to include the motto In "God We Trust" on the back.

United States Notes were discontinued in the late 1960s, and $2 bills were converted to Federal Reserve Notes in 1976. As part of the Bicentennial, the reverse was completely redesigned and now shows an interpretation of Trumbull's painting of the signing of the Declaration of Independence.