[Oh God Spiders No]

The Impossible Game's first level kind of does this. The music is catchy, but rather subdued and unobtrusive. You'll probably die a few dozen times figuring out the timing of your jumps, making it over several basic but increasingly dastardly arrangements of obstacles.

And then.... once you've passed the requisite number of introductory tests the music suddenly explodes, the bass drops in hard, and your little square is suddenly faced with an almost endless series of stairs that bring it far up into the sky.

The sudden introduction of high intensity music and surprising verticality is a real shock. I first played this game as one of eight complete novices and the first time one of us got to the stairs the room exploded into cries of surprise and amazement. It's one of the best moments I've had in videogames.

Later levels emulate this, as well. They each have their own little gimmick that doesn't kick in until the music picks up a few stanzas in.
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[Oh God Spiders No]

Almost every interactive puzzle game probably has something like this. Lighthouse, a game about fixing old machinery in a long-dead civilization, starts with you checking your answering machine and then finding a set of car keys before leaving your house.