In Neverwinter Nights expansions, you can play a Dragon Disciple who becomes a half-dragon upon reaching level 10 in that class. Overall, I tend to find it underpowered though (some stat buffs, limited use breath weapons, immunity to fire and paralysis and some other minor stuff if I recall, it's ok, but you can get far better by leveling up in some of the other prestige classes)

In Rogue Legacy, you can play a dragon-like (half dragon?) class when you reach the top of your tech tree, but again, it's very disappointing (useful to reach hard to get green chests, that's about it).

EDIT:

Now that I think about it, if you include games where you can morph into a dragon:

- In Neverwinter Nights, the shifter's ultimate morph is dragon form

- In Shadow Caster, the (arguably) second most powerful morph is a dragon-like form that can fly, spit fireballs and attack in a spear-like fashion with its tail

- In the Last Federation, you play the last dragon, though you play inside a spaceship and it's more of a strategy game with roleplaying elements thrown in.

I of the Dragon comes to mind - http://store.steampowered.com/app/279720/

Hoard isn't an rpg, but you get to be a dragon - http://store.steampowered.com/app/63000/

I found this while looking around too (looks kind of casual, but claims its an rpg)

Dragon: A game about a Dragon - http://store.steampowered.com/app/351150/

Also found this

Dragon: The Game - http://store.steampowered.com/app/305960/

Blue Dragon

The core mechanic in Blue Dragon is the use of magical "shadows", with each playable character having a distinct shadow modeled after either a dragon, a phoenix, a bat, a minotaur, or a saber-toothed tiger. Each shadow can be assigned to a single character class (from a number of such classes) at a time, taking on the attributes and abilities of that class.

https://en.wikipedia.org/wiki/Blue_Dragon