Once a watermelon has hit the ground it will explode, just as if it was a Grenade.
Watermelons can also be useful: if you can get a monkey to throw one at you during your faceoff with the stone golems inside the temple, the exploding fruit can knock out the golem instead of you, without having to try tricking them to get into the trap doors on the floor.
Outside of the Aztec Ruins, they also appear several times through out Siberia, though they pose no threat and are simply there for comedic relief, as you can shoot and destroy them. They also appear several times in challenges, namely Monkey Mayhem in TS2 and Melon Heist in TS:FP. Both missions are nearly exactly the same- you must shoot the melons out of the monkeys' hands while not shooting the monkeys themselves.