Below's a list of the 16 unassisted triple plays in major league history (with "player" being the fielder who turned the play, NOT the batter who hit into it):
| Player | Position | Team | Date |
| Paul Hines | CF | Providence Grays | May 8, 1878 |
| Neal Ball | SS | Cleveland Naps | July 19, 1909 |
| Bill Wambsganss | 2B | Cleveland Indians | October 10, 1920 |
| George Burns | 1B | Boston Red Sox | September 14, 1923 |
| Ernie Padgett | SS | Boston Braves | October 6, 1923 |
| Glenn Wright | SS | Pittsburgh Pirates | May 7, 1925 |
| Jimmy Cooney | SS | Chicago Cubs | May 30, 1927 |
| Johnny Neun | 1B | Detroit Tigers | May 31, 1927 |
| Ron Hansen | SS | Washington Senators | July 29, 1968 |
| Mickey Morandini | 2B | Philadelphia Phillies | September 20, 1992 |
| John Valentin | SS | Boston Red Sox | July 8, 1994 |
| Randy Valarde | 2B | Oakland Athletics | May 29, 2000 |
| Rafael Furcal | SS | Atlanta Braves | August 10, 2003 |
| Troy Tulowitzki | SS | Colorado Rockies | April 29, 2007 |
| Asdrubal Cabrera | SS | Cleveland Indians | May 12, 2008 |
| Eric Bruntlett | 2B | Philadelphia Phillies | August 23, 2009 |
A few notes:
Hines' triple play is disputed. According to information found on cbs.sportsline.com, runners were on 2nd and 3rd when Hines made a running catch and touched third base for the second out, before throwing the ball to second base for the third out (for what might be a triple play, but NOT an unassisted one). However, many claimed that both runners were past third base when Hines touched it, which would have given him an unassisted triple play, according to the rules of the day.
Due to this uncertainly, Hines is sometimes excluded from lists and counts (leading some sources to say there have been 15 unassisted triple plays in history, instead of 16; I have emailed the Research staff at the Major League Baseball Hall of Fame for clarification).
Wambsganss's triple play was in the World Series. Velarde also turned a triple play during spring training (which, being in an exhibition game, doesn't count as an official record) the same year as his regular season play.
Almost all unassisted triple plays come on a hit-and-run play with runners on first and second (Hines' being one of the notable exceptions). All but three of the them were made by second basemen and shortstops (Hines was a centerfielder, Neun and Burns were first basemen).
Burns, Valentin and Tulowitzki are the only players in Major League Baseball history to have both turned an unassisted triple play and hit for the cycle in their careers.
Note that Cooney and Neun accomplished the feat on consecutive days. Neun had read about Cooney's UTP and joked to teammates that he was going to do something similar during the next game. As luck would have it, he did! And more than 40 years passed before the next unassisted triple play!