The baseball bat is used many times, as it is a very effective weapon in hand-to-hand combat. It is first used in Running Man by a Morello gangster destroying Tommy Angelo's cab. You get to use it the first time in Molotov Party to destroy a few Morello cars parked behind Morello's Lounge Bar. It is seen again in the missions Sarah, Better Get Used to It, Visiting Rich People, Bon Appétit, and Just for Relaxation.
You can find more real world information about the baseball bat on its Wikipedia page.