Can cats eat bananas?
Bananas are non-toxic to cats and safe for a cat to eat in moderation. 
Bananas are rich in vitamin B6, manganese, vitamin C, potassium and dietary fibre. However, because cats have evolved to consume a meat diet, they are not able to digest plant material as effectively as omnivores and herbivores.
Snacks should make up no more than 10% of a cat’s diet. Cats are obligate carnivores which means they need to consume meat to survive as they are unable to manufacture some vitamins, amino acids and fatty acids and must obtain them in their pre-formed state from the meat and organs they consume. Some cats do enjoy the additional non-meat treats including fruit, vegetables, eggs, cheese and yoghurt.
How to feed banana to a cat
Ripe bananas can be fed raw, frozen pieces or air-dried chips which make a great snack.
Fibre may be of benefit for mild constipation, although there are more effective foods and treatments. Overall a banana offers little in the way of nutritional benefit.
The ripe fruit of a banana is safe for a cat to eat, but use caution when feeding banana-flavoured foods to a cat as they may contain additional ingredients which are toxic to cats.
Stick with the flesh and do not feed the tough peel which can potentially choke a cat.
When not to feed banana to a cat
Cats who are on a prescription diet, as the nutrients in the banana may interfere with the diet. For example, a cat on a low-iodine diet to manage hyperthyroidism or a cat on a food trial as other foods (including snacks such as banana) may invalidate the trial.
Cats who are on a calorie-restricted diet to lose weight.
Because there is very little nutritional benefit to eating bananas, limit the frequency and amount. Bananas should not replace a well-balanced and nutritionally complete cat food. Keep them as an occasional treat, once or twice a week.
Can cats eat other fruit and vegetables?
Yes, several fruits and vegetables are safe for cats to eat, which includes strawberries, blueberries, apples, pears (seeds removed), melon, broccoli, zucchini, cucumber and corn.
See here for a full list of fruit and vegetables cats can eat.