Watermelon and many other fruits and veggies are safe for dogs in moderation. My dog loves apples, bananas, pears, carrots, and things like that. I give them to him for a low calorie treat once in awhile.
Just keep in mind that dogs don't always digest plant matter very well, so they don't really get much nutrition out of eating fruits/veggies and if you feed too much it can cause digestion upsets.
Also, if you're going to give things like this for treats it's a good idea to research and make sure you know what plants/fruits/veggies are not safe for dogs. Grapes and raisins, for example, are toxic to dogs. Don't let them eat pits or seeds from fruits either. Rhubarb, tomato plants (the actual leaves, not the fruit), onions, garlic, and avocado are all toxic to dogs. Those are just examples.
But watermelon is safe and many dogs do enjoy it! It's a nice refreshing treat especially in the hot weather, as it contains a lot of water and can help keep your dog hydrated.