There's actually some pretty nightmarish stuff in a lot of the Sonic Games, especially Sonic Adventure 1 and 2 where things got a little heavier than the Genesis trilogy:
-Sonic CD: The Japanese game over music is basically "Awww, you lost. That's okay, you can always try again." The North American music is basically "YOU ARE NOW TRAPPED IN THE ICY BLACK GRIP OF DEATH AND SOON THE REST OF THE WORLD WILL JOIN YOU!! ! YOU FAILED! FAILED HORRIBLY! WELCOME TO HELL!! !" The NA boss music is pretty creepy too.
-Sonic Adventure 2, which shows Maria's being shot to death while with Shadow on the Ark, and then Gerald Robotnik about to be executed after he went insane when he learned that she had died, and then Shadow presumably dies after he and Sonic save the world. The music certainly also helped fit the chillingness - chillingness isn't a word? It is now.
In Sonic Spinball for the Genesis the first boss has creepy Robotnik-heads that puke out magma (some people think it's blood), another is a robotic womb-like contraption that shows the animals being turned into robots (with a window in it so you can see the animals looking like x-rays from radiation or maybe being electrocuted). And it's called the Veg-o-Matic. Huh?? Also the game over music sounds a bit like it's saying OHMYGOOHMYGODOHMYGODNONONONONOOO!
Other games I can think of are:
Game Over Return Of Ganon from The Adventure of Link. Who would have thought a laughing cartoony-looking pig could induce such nightmares?
It's more of an E-rated version or a parody of a typical horror game, but Luigi's Mansion had some pretty creepy stuff, like Bogmire the boss ghost. The Beta version was even creepier because the game over screen showed a zombie-like Luigi with baggy, pupiless eyes! Actually the game originally had a timer where you had to rescue Mario before sunrise. If you didn't the mansion would vanish with Mario still inside which makes Luigi so depressed he ends up looking like that, or the ghosts turned him into a zombie, or both. I'm actually glad they left that out because it was just too much~!