Once Upon A Time is the one I have played quite a bit of.
I have played some GURPS as a story game, the mechanics are neutral.
I have played D&D 4E as a roleplaying game. The design leans toward the narrative/story side but it doesn't have to be played that way.
Yeah, Once Upon A Time isn't a rpg. But then, no one thinks it is, afaik. It is indeed a storytelling game. GURPS is a simulationist rpg. How did you run it to make it into a 'story game'? D&D 4e is a traditional rpg with more emphasis on gamism than simulationism. No narrativism at all, as far as I'm aware.
None of those are what I would've suspected one might mean by 'story games'. Well, except Once Upon A Time. But, like I say, no one thinks it's an rpg.
I thought you were talking about games that bill themselves as rpgs but are heavily narrativist, such as Prince Valiant (the first narrativist rpg) and Forge type games such as My Life With Master or Dogs In The Vineyard. Or maybe Vampire 2nd ed which has a chapter on storytelling which includes techniques similar (or identical) to those in DMG 2 such as flashbacks, dream sequences and foreshadowing.
I thought you might also be talking about player control of elements outwith the PC's control, which are not, imo, necessarily narrativism, such as in James Bond 007.
EDIT: The only other person I've seen using the term 'story games' to refer to what other people call roleplaying games was howandwhy99. He seemed to be using it to mean any rpg published later than 1990. I guess I've been assuming that you and Ariosto are cut from a similar cloth, which is probably very unfair. Howandwhy's definitions are highly eccentric, I don't even think any edition of D&D would've fit his weird definition of what a roleplaying game is.