Triples are pretty fun. Usually, they happen for one of two reasons. The first is when a really fast guy gets a ball into the gap and speeds his way into third. The other is when a fielder royally messes up, and the defense can't clean up the mess until the batter is at third.
The record for triples in one game is four, and both happened a very long time ago. George Strief did it in 1885 in the American Association, and Bill Joyce did it in 1897. After that, there is a many-way tie for second place with three, a tie that includes the likes of Yasiel Puig, Willie Mays, and Baby Doll Jackson.