When hamsters are comfortable and content, they will not bite. Hamsters are quite docile creatures whose top priorities are eating and sleeping. When they do bite, it will be for two reasons, they are either scared or the owner has food like peanut butter on the fingers.
Hamsters can get scared when a new owner is bringing the hamster home. The ride back will be nerve-racking as most of the time they are put into a small box for transport and this will cause the poor hamster to become claustrophobic. At that moment is when the hamster is most prone to purposely biting someone's finger. The new owner will have to take great care in taking the hamster out of the box and putting it into the hamster cage. Even in the first few hours in its cage, the hamster might still bite as it is in unfamiliar surroundings. It is best to leave the hamster in the cage for a day with food available at all times. Let the hamster eat and take a nap. The hamster will calm down and will come to know that the hand that feeds it is not an enemy.
With boys you always know where you stand. Right in the path of a hurricane. It’s all there. The fruit flies hovering over their waste can, the hamster trying to escape to cleaner air, the bedrooms decorated in Early Bus Station Restroom.
—Erma Bombeck (20th century)
The second reason why most hamsters might bite the owner is because the owner has food or condiment covering the fingers. A hamster will think the finger is food and will bite on it, but it won't hurt nearly as much as a hamster biting out of fear. If you feed your hamster by hand, use your palm to hold out the food. As long as the owner keep the hands clean from jams and anything sticky, the hamster will not bite.
Last but not least, female hamsters are generally more aggressive than their male counter-parts. So if you want to take all precaution in not getting bit by a hamster, then consider purchasing a male hamster.