1. John C. Calhoun resigned December 28, 1832. Calhoun was Vice President for nearly eight years under President John Quincy Adams and President Andrew Jackson but fell out with Jackson over the tariff and nullification (Calhoun’s theory that an act of Congress could be declared void by a state legislature). Calhoun was not re-nominated to run with Jackson in 1832 and ran for the Senate instead. After the election, he resigned as VP to take his Senate seat.
2. Spiro T. Agnew resigned October 10, 1973, and then pled nolo contendere (no contest) to criminal tax evasion for income he allegedly received in the form of bribes while governor of Maryland. Agnew was Vice President under President Richard Nixon.