Robert Crittenden was born near Versailles, Kentucky.
Crittenden served as Secretary of Arkansas Territory from 1819 to 1829. Crittenden served as acting Governor of Arkansas while James Miller was delayed for an extended period in route to Arkansas. Crittenden called the first legislature into session and took responsibility for organizing the new territory. Crittenden was never appointed Governor of the territory but amassed considerable political power during his ten years as territorial secretary. Crittenden was a primary leader in preparing the territory for statehood.
Crittenden served as United States Commissioner for the 1824 Treaty with the Quapaw Indians.
Robert Crittenden was the son of John Crittenden who was a Major in the Continental Army and a member of the Virginia House of Burgesses, the brother of United States Senator John Jordan Crittenden, and granduncle of Thomas Theodore Crittenden, Jr. who was Mayor of Kansas City, Missouri.
Crittenden mortally wounded Representative Henry Wharton Conway in a duel on 29 October 1827. He died in Vicksburg, Mississippi.
Crittenden County, Arkansas is named for Robert Crittenden.