I keep being drawn back and forth between the Zelda and Fable series. I want to say Occarina of Time because of how it's affected gaming for me, being my first real game... but I think I would have to go with the original Fable (well the Lost Chapters version since it's an expansion of the original Fable) because of the way you can shape your own adventure.
Your character changes with your choices, you hone your skills through the way you play. If you tackle your enemies hand to hand, the experience you receive will enable you to focus on strenght, physique and the like. If you use a lot of magic in battle scenarios, the experience you receive will enable you to hone your existing spells, or enable you to learn new spells. If you focus on skill, like battling from a distance, trading, stealing, the experience you receive will enable you to hone these skills.
And in addition to building your character's strengths, you also define your character's moral compass. Good deeds push you towards "good" and evil deeds push you towards "evil" and a balance between the two keeps you neutral. Depending on where you are on the scale between pure "good" and pure "evil" your character will reflect it.
You basically build your character's personality through your actions, from their strengths to their alignment, down to their sexuality. By accessorizing your character with clothing, haircut, facial hair, tattoos... you can attract people, repulse people, scare people... Your interaction with characters can define this as well... What you eat can even change your character's physique...
Possibilities and consequences evolve and expand with the games that follows, but not revolutionarily so. That's why I have to go with the original Fable as the best game. Because it already has in place so many features, so many options, a great story and a ton to do both within and aside from the story itself...
[video=youtube;X4f1eDrqt_w]http://www.youtube.com/watch?v=X4f1eDrqt_w[/video]