Most parrots are sociable with members of their own species, as long as they have enough personal space, and somewhere to retreat to if arguments turn nasty. Bickering is part of parrot life, as with humans.
Things get trickier once you start to mix and match different parrot species. In general, Budgies, Cockatiels, Hanging Parrots and Conures are said to be the most peaceable and socially liberal of the family.
Some parrots get along, but not all of them do!
At the other end of the scale, Cockatoos, Caiques, Lories, Lovebirds and Macaws are renowned for their aggression – especially towards newly introduced members of a different species. A mild bout of bad-spirited parrot fighting can result in lost feathers; a violent bout can end in serious injury or even death.
The rule of thumb is to check with your seller whether your intended mix of birds is suitable. Never introduce a new bird – even one of the same species to your existing birds – without asking advice.