Rare

Asdrubal Cabrera Turns Unassisted Triple Play
Uploaded by Machochip

Asdrubal Cabrera achieved the rarest stat line in Major League Baseball yesterday. He recorded the 14th unasisted triple play ever in Major League history. To give you an idea how rare this is, consider that 17 perfect games were pitched in the same 132 year span.

Unlike a perfect game though, the unasisted triple play is much more serendipity than skill, requiring these exact circumstances: a hit-and-run with two runners on and no outs, and line drive hit to either the second baseman or the shortstop.

UPDATE: Ok, according to Wikipedia, four home runs in one game is the rarest stat line [EDIT: but it says 15 have been recorded, so UTP has to be more rare with only 14]. I don't know what "counts" as a stat line but one could argue that taking a perfect game to extra innings only to lose is even more rare. It has only happened once. Harvey Haddix pitched 12 perfect innings only to lose the game in the bottom of the thirteenth.

UPDATE II: Had to change video feed, MLB made YouTube take it down.