The Golden Sun series, (the first two, third one was blah), and Final Fantasy Tactics (PS or GBA, whichever you fancy).
These were games that every cutscene could be the end, (actually, the first Golden Sun ended out of nowhere) and I found myself saying "Don't be the end, don't be the end" instead of actually reading dialogue.
I think RPG's tend to lend themselves to this kind of reaction, most games these days rely so little on the single player experience, there is no end for most of these FPS's, Sports games, Racing games, etc. So I only see Platformers and RPG's ever falling in to this category in the future.
On a side note, who thinks that Final Fantasy Tactics would be a FANTASTIC launch title for the Wii U, being that as it will take full advantage of the second screen, and only be single player (no arguing over the tablet)?