I voted to close the question as it was originally written. The wording in the question doesn't limit the answers at all. It could be any sport in the world, at any level. The fact that the answers just kept coming in from sports all over the world (including a list of 18 times that it has occurred in Cricket*) indicated to me quite clearly that the question was a list question that was way too broad. I also left a comment indicating this.
After the question was edited by @pacoverflow, the original question author, to limit it in scope to the four U.S. major leagues, I voted to reopen and deleted my comment.
I still think that the question is too broad when it is not limited to a finite number of sports, and I would like to see the question reverted back to Revision 2.
*The 18 father/son Cricketer pairs were all fathers and sons who played in the same match, which means that the number of father/son pairs who simply played cricket at the same time is probably much higher.