Usually it happens when Cthulhu learns his destiny by listening to the narrator; either that, or when he starts complaining about the tutorial. Regardless, few RPGs can boast that sort of magnetic attraction at the outset; and while Cthulhu Saves the World ultimately drags a bit, its self-aware one-liners and fourth-wall breaking humor is consistently excellent. Laughter, in this case, doesn't cure all ills, but it comes pretty close.
The funny thing is that humor isn't exactly a rarity in RPGs; it's just the legitimately funny stuff that's hard to find. A lot of it is over the top, such as this classic, or simply not all that interesting. The Tales vignettes are cute, but shallow. The Fire Emblem: Awakening support conversations, much as I like that game, frequently induces a sustained bout of eye-rolling.*
(*Note: Your mileage will vary, as with all humor).
Some RPGs have managed to get it right though. And when they do, good things tend to happen. The mood gets lighter, the characters seem brighter and more interesting, and the reams of dialogue that accompany every RPG suddenly becomes downright interesting. Here are a few examples:
Fallout: A dark, ironic sense of humor helped to lighten the dark post-apocalyptic mood. Being able to talk The Master into killing himself wasn't precisely "funny," but it was shocking enough to inspire its own brand of laughter.