Yes, ants eat termites.

More Info: Ants are the natural enemies of termites.  Most ant species eat insects both living and dead including termites.

What Else Do Ants Eat?

Ants are not a finicky bunch.  Depending on the species, an ant diet can consist of other insects, dead or alive, meats, sweets, and honeydew.

Carpenter ant: The carpenter ant sticks to the basic diet of insects, meats, sweets, and honeydew.  Though the carpenter ant does not eat wood, it does chew it into sawdust in order to tunnel.

Cornfield ant: Eats a very basic diet of insects, sweets, and honeydew.

Field Ants: Simple diet of insects, sweets, and honeydew.

Larger Yellow Ant: Subsists on honeydew.

Pavement Ants: Feed on insects, meats, sweets, breads, and pet food.

Pharaoh ant has a decidedly interesting sense of taste.  The pharaoh ant will eat greasy, fatty foods, sweets, dead insects, and oddities such as soap and toothpaste.

Thief Ants: Eat greasy, protein foods including peanut butter, nuts, meats, and cheeses. Will eat sweets.  Likely named for their small size and ability to enter most any container.

Interesting Fact: Fire ants gather their dead and place them in piles called middens.  Middens are stored in underground chambers of an ant colony until weather permits them to be moved outside.