Whether hamsters can live together depends entirely on the species. Syrian hamsters are strictly solitary and must always be housed alone after reaching approximately eight weeks of age. Dwarf hamster species may cohabitate under certain conditions, but success is never guaranteed.
Syrian hamsters, also called golden or teddy bear hamsters, are territorial and will fight other hamsters aggressively. These fights can result in severe injuries or death, even between siblings that grew up together. There are no exceptions to this rule. One Syrian per cage, always.
Dwarf species including Winter White Russian, Campbell's Russian, and Roborovski hamsters are more social and may tolerate same-sex companions if introduced properly. The best chance of success is housing littermates that have never been separated. Introducing adult dwarfs that were previously housed alone rarely works and often leads to fighting.
Even compatible dwarf hamsters can turn aggressive suddenly. Triggers include reaching sexual maturity, illness that makes one hamster vulnerable, an enclosure that is too small, or competition over food, water, or nesting resources. Always have a second enclosure ready as a backup in case separation becomes necessary.
If you house dwarf hamsters together, provide a spacious cage with at least 775 square inches of floor space, multiple food dishes, two or more water bottles, separate hiding houses, and multiple wheels. Resource competition is a primary cause of aggression.
Watch for warning signs including chasing, squeaking, one hamster hoarding all the food, one hamster always being excluded from the nest, bite marks, or fur loss. These indicate the pair is not working and separation is needed immediately.
Chinese hamsters are often grouped with dwarfs by pet stores but are actually semi-solitary and are better housed alone. Their temperament is unpredictable in pairs.
Never house mixed species together, and never house males and females together unless you are prepared for rapid, repeated breeding with litters of six to twelve pups each time.