Parakeets, or budgies, would wholeheartedly agree that "one is the loneliest number." They love companionship, and they only need the right introduction to share their space with a stranger.
Parakeets are very social animals and are happier when they feel they are part of a flock and not isolated. A lonely parakeet can become very depressed. A parakeet will consider humans part of his flock, but if his people are not interacting with him frequently he will get lonely. Introducing a second parakeet can cheer up a lonely single one, if the two are able to bond without becoming territorial.
Although they aren't quite as outgoing as many larger parrots, parakeets still form close bonds with people and other birds. Two strange parakeets put together may not immediately form a bond, but over time they will usually become good friends and treasure their bond even over the one with their owner. The exception to this is two adult females. Although they might get along, adult females tend to be territorial and are more likely to fight than a pair of males or a male and female pair.
Two parakeets who are strangers to each other should not immediately be placed in the same cage together. Introduce them slowly, in neutral territory, and allow them to get to know one another. It is best to begin by giving each parakeet his own cage and placing the cages side by side. Allow them to meet each other in a play area that is not located in either of their cages. As they become familiar and friendly with each other, gradually transition them to one of the cages by allowing them to spend more and more time in the cage together.
While two strange parakeets might become closely bonded and spend most of their time together, a larger cage is necessary for two birds than for one. Provide enough space so they can get away from each other if they are not feeling social. This is especially important in a male and female pair, where the female may get tired of the male's advances.