Tch. Young'uns. I remember the first time I died by HP loss in Ninja Gaiden (for the NES, thankyouverymuch) and Ryu just sat there in his hurt pose while the game played a short elegy for my fallen ninja.
"Oh, look, look, you died. I'm playing a synthesizer violin for you."
If I had to go with something more recent, I'll take Jak and Daxter. Falling in black eco would always be amusing; You don't even sink, you just burst. Because it's DEATH WATER! DEATH WATER! Stop falling in the DEATH WATER!
*Waits to see if anybody would actually catch that reference*