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):

Date         Player           Team           
05/08/1878   Paul Hines       Providence Grays
07/19/1909   Neal Ball        Cleveland Naps
10/10/1920   Bill Wambsganss  Cleveland Indians 
09/14/1923   George Burns     Boston Red Sox 
10/06/1923   Ernie Padgett    Boston Braves    
05/07/1925   Glenn Wright     Pittsburgh Pirates
05/30/1927   Jimmy Cooney     Chicago Cubs
05/31/1927   Johnny Neun      Detroit Tigers 
07/29/1968   Ron Hansen       Washington Senators
09/20/1992   Mickey Morandini Philadelphia Phillies
07/08/1994   John Valentin    Boston Red Sox
05/29/2000   Randy Velarde    Oakland Athletics
08/10/2003   Rafael Furcal    Atlanta Braves
04/29/2007   Troy Tulowitzki  Colorado Rockies
05/12/2008   Asdrubal Cabrera Cleveland Indians
08/23/2009   Eric Bruntlett   Philadelphia Phillies

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 came 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 and Valentin are the only two 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!

I was present at Yankee Stadium on May 29, 2000 when Oakland A's second baseman Randy Velarde performed the feat listed above, and I remember it well. I'll describe my experience of it, and the reaction of the fans around me, as it was pretty interesting.

First, it's worth noting that the game took place on a Memorial Day Monday, and before the game the fans had enjoyed witnessing the Yankees' World Series ring ceremony. Yankee icon Yogi Berra handed out the rings commemorating the team's 1999 World Series victory over the Atlanta Braves. I say it's worth noting because Velarde spent 9 seasons as a Yankee before becoming a free agent and leaving after the 1995 season, thus just missing the Yankees' eventual run of four World Series championships. So Velarde had to watch his former teammates receive World Series rings -- bittersweet, I would think. Incidentally, Velarde also homered in the ninth inning of that game, accounting for the Oakland A's only run.

Fast forward to the bottom of the 6th inning where it's 1-0 Yanks. A's pitcher Omar Olivares walks Paul O'Neill to lead off the inning, and Bernie Williams follows with a triple off the wall in right, scoring O'Neill. Olivares then plunks Tino Martinez, bringing up Jorge Posada. Posada hits a double-play grounder to Velarde at second, but Velarde boots it! Williams scores, and now the Yanks have Posada on first, Martinez on second, and still nobody out. So you see, it's Velarde's own error that sets up his historic moment one batter later.

All right, picture the scene, if you will: You're at Yankee Stadium enjoying a ballgame on a long holiday weekend. Maybe you've had a couple of beers, a couple of hot dogs. You're taking it all in. It's a tightly pitched game so far, but your team finally has a bit of a rally going, scoring two runs that inning, two more runners on base, and still nobody out. It seems a foregone conclusion that a big inning is about to unfold.

And yet...

The next batter, Shane Spencer, works the count full. Yankees manager Joe Torre, looking to ignite the offense, and, ironically, perhaps avoid a double play, sends both runners. Spencer lines the ball sharply to Velarde who catches it (one out), tags Posada, who had been running all the way and was just a step or so away from second base (two outs) and then steps on the bag to triple off Martinez, who was practically at third base (three outs). All this takes place in literally about a second.

Now keep in mind that you're at the game and maybe you don't have the best seats in the world, so you're a little far away from the action. There are no announcers, nobody doing play-by-play like when you're watching a game on TV, so you're on your own in terms of figuring out what's going on. One minute you've got two men on and nobody out, then there's a soft liner and some commotion around second base, and suddenly everyone's trotting off the field! What just happened? You can hear the confusion among the fans, as if 40,000 people just uttered a collective "Huh?" Also keep in mind, there's no instant replay, no nothing. I kind of had to re-visualize the play in my own memory to understand what had just happened, and once I figured it out, I was pretty pleased. An unassisted triple play. I knew it was rare, but just how rare, I didn't know until later.

It's actually one of the rarest events in baseball -- rarer than a perfect game, rarer than a four-homer game, rarer than an inside-the-park grand slam. As the writer above notes, the Hines play is disputed, and the Wambsganss play was in the World Series, so what I (and 40,000 others) witnessed that day had only happened nine times in regular-season history before that. The ball, and Velarde's glove, are now in the Baseball Hall of Fame in Cooperstown, NY. Exciting stuff for a baseball geek like me.

(I should conclude by mentioning that Yankees pitcher Andy Pettitte pitched a complete-game two-hitter for a 4-1 win that day. The Yankees would beat these same Oakland A's in the divisional series later that season on their way to winning the 2000 World Series against the Mets -- the famed "Subway Series.")