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Fire Emblem: Awakening, JP Version.
Tales of Vesperia PS3 is a close second.

I have never done so. Not once.

If I ragequit, I just express it through other, non-physical means.

Original NES Super Mario Bros.
But I got so frustrated I stopped.

I didn't really get into it until the Playstation that my cousin had and he was playing Final Fantasy VII.

Final Fantasy X for the PS2.

Physical. There's just something about physically holding the game. I did this for Fire Emblem: If Special Edition, instead of just downloading it off the eShop the minute it got released.
Patience...