They all also feature main characters who struggle against totalitarian societies. In 1984, Winston Smith realizes that he is being controlled and tries to rebel against Big Brother. Although he ultimately loses to Big Brother and O'Brien, he represents a human's need for freedom of thought and being.
Similarly, in Fahrenheit 451, Montag fulfills the role of a "Winston Smith." He begins to question what he and the rest of his society have been indoctrinated with and eventually stages his own revolution. In contrast to Winston, he actually meets with a success of sorts at the novel's end.
Brave New World features a similar character--John the Savage--who was conceived mistakenly (seemingly an act of inintentional rebellion itself) and who tries to fight against the regime. In the end, however, John meets his demise through hanging.
While there are certainly many similarities among the three novels, another significant element is the misuse of technology, whether it be Room 101 and the telescreens in 1984 which torture and spy on humans or the television walls in Fahrenheit 451 or the abuse of reproduction advances in Brave New World. All three authors stress the tendency of totalitarian regimes to control the populous with technological advancements.
To me, the main thing that these three books have in common (or the societies in them) is that they have all been drained of real human emotions. If you think about it, none of the three societies have people who really love and care about each other.
I guess the other thing I see is that all three dystopian societies try to control the thoughts of their people to some extent or other. They do not want people to think very much for fear that they will become restless and rebel.