While researching steals of home, I discovered this page at Baseball Almanac, detailing every instance a player stole second base, third base, and home plate in the same inning. It has happened 50 times since 1899, though only 11 times since 1928. Dee Gordon was the last player to steal for the cycle, on July 1, 2011.
The career record for stealing for the cycle is 4, held jointly by Ty Cobb and Honus Wagner. Cobb also holds the record for career steals of home plate, with 58, and holds the single-season record of 8 (1912). Wagner is one of eleven players to steal home twice in the same game, a feat Cobb never managed.
Four of Cobb's steals of home plate occurred during his end-of-career stint with the Philadelphia Athletics. Because baseball records from before The Living Room Era are spotty, I couldn't find out if Cobb holds the A's single-season record for steals of home. He might, but there's a pretty good chance Eddie Collins beat that during one of his two stretches with the Mack Men.
Team Stolen Base Records (including single-season and single-game records for stealing home)