I have split 10's to get rid of people at a table. I have also not split aces, split 2's, 3's, 4's etc to clear the table. You also do it to burn cards.
I have also split 10's if I had a high plus count and had a lot of money on each hand (playing 4 hands for example) and got dealt:
Hand 1: 10,10
Hand 2: 10, 5
Hand 3: 7, 6
Hand 4: 10, 10
and the dealer had a 7 or 8 showing. In this case I would split both 10's to save the other 2 crappy hands. I would only do this with a real high plus count.