I've had dragons as cohorts, allies, recurring enemies etc. and once I had two dragon PCs. The other players had no idea they were dragons, though. This was a campaign with a group of mostly newbie players.
Two guys kept getting killed all the time, because they simply didn't care about their characters; PC death was simply a chance to make a new PC to them. When they got themselves killed on a (mostly) uninhabited group of remote islands, I told them there were only two options for their new characters: Either play members of the clan of manically depressed dwarves living on one island, or they could be song dragons (from Monsters of Faerun).
The shape-changing song dragons like to live incognito in human societies, but one of these islands was where they came to mate and raise their little wyrmlings. Since song dragons can only take the shape of a human woman, I figured they have to assume their real shape to mate with their own kind.
Obviously the players preferred playing dragons over playing manically depressed dwarves. They told the party they were escapees from a society of amazons, and persuaded the others to stay away from the island were the 'amazons' lived. The players loved their new characters and did all they could to keep them alive, which was just the effect I was hoping for when allowing them to play dragons.