This is a bit of a stretch, but in Fire Emblem: Path of Radiance, there are characters that are your allies who can transform into dragons. But it's a strategy game, so it's more like you just move them around a map and watch the battles play out without actually controlling them.
And Radiant Dawn gives you both of those dragons at once, plus the dragon prince and another dragon, all playable at the same time. You have a point though on the whole strategy game thing.
Don't they all die/turn evil in the end?
I'm not sure it matters, but I saw this one game at a pawn shop called Scaler, which I know nothing about other than the fact that the main character is a dragon, or at least the box-art made it look like that. From the cover, it looked to me like a crappy Spyro ripoff, but since I've never played it or know anyone who has, I can't say how bad or good it is.
There's this Dungeons and Dragons game for the NES where you can play as a bronze, silver, or gold dragon.
Then a Namco game named Dragon Spirit (or something like that) where you can play as a dragon, but it's pretty average. ...Better than the Dungeons and Dragons game, though.
The Shining Soul series has anthro dragons as playable characters if those count.
There's also a Japanese game named Emerald Dragon where you START OUT as a dragon, but soon turn into a boring human 10 minutes into the game. Not sure if it's worth a mention.
That's all I know for now.
Edit: Apparently, Scaler DOES have a fanbase, so I guess it's not all that bad, but unfortunately the game just stares a lizard, not a dragon, so it doesn't really count, I guess.
