The Short Answer:
Although there are some foods that dogs cannot eat, bananas are not one of them. In fact, bananas can be used as a treat for dogs. Most dogs will love the sweet taste that bananas have, and so they are a great way to help train a dog, or to give your friend a reward for their good behaviour.
If you are giving a dog some banana, you should know that it is high in amino acids, electrolytes, minerals, vitamins B6 and C, potassium, fiber and manganese. THis is healthy for your dog, but because of high levels, bananas need to be given in moderation, otherwise it can lead to bloating, and bad runs.
The First Time:
The first time you give your dog any food, you should give only a very small amount. This is because like humans, dogs can have allergies to foods. Give your dog a piece, and watch him or her for about 10-20 minutes. If he or she starts sneezing a lot, coughing, or seems to act strangely, do not give any more. If your dog acts strange for over 1h after the banana is given find a vet to go to quickly. If your dog is fine, feel free to give him or her a couple slices.