While I wouldn't call them bosses, there's the majority of the ghosts and other creatures in the point-and-click adventure Uninvited. Shadowgate is another especially scary one; Deja Vu, as well as the sequels, are definitely eerie, but they aren't the sort of thing that burns into the back of your head.

NalaTheLion : While Soul Reaver isn't exactly a horror game, it does have things that are easily described using such tasty words as 'grotesque' or 'vile'. It's more of a puzzle game, but it still has elements that can be pretty scary. For example, in the area where you fight Zephon (the Silenced Cathedral), you have to deal with his offspring, who are a sort of mutated vampire that developed spider-like traits and powers. That they climb all over the walls, which makes it hard a all Hell to see them, and they make this spine-tingling 'clackclackclack' noise as they step, it can really freak you out; I think they turned out a lot scarier than they were intended to be. 

If you're okay with just a link to the pictures instead of actually putting them up on here, I'll show you.

Concept art for Melchiah, and the video of the fight with him.

http://i480.photobucket.com/albums/rr167/mappster71/skinrb051.jpg

http://www.nosgoth.net/Soul_Reaver/conceptart/Melchiah1.JPG

http://www.youtube.com/watch?v=QuHwPfJC-Hc

Here's art for Zephon, and his fight video.

http://images1.wikia.nocookie.net/__cb20120226151709/legacyofkain/images/0/05/SR1-Character-Zephon-Ayala-WallBoss1.jpg

http://www.youtube.com/watch?v=6QdVHw1y0NU

Rahab's picture, as well as his video.

http://www.nosgoth.net/Soul_Reaver/dialogue/Rahab.jpg

http://www.youtube.com/watch?v=3qLIcX7vcDw

There are a few others, but they're not as especially freaky. Although, if you're into Lovecraftian things, the guy who's coaching you through all of this is a being known as the Elder God, who looks kind of like Yog-Sothoth.

inb4motherfans

Every other person here is going to say Giygas, I just know it. While I don't disagree that he's scary, I don't think he's the scariest boss out there.

The ones that are, in my opinion, some of the most horrifying, are the clan leaders from Soul Reaver. Melchiah first and foremost; he's basically a mass of flesh and bone stitched together, entire human bodies mashed into one clump that consists of a very stretchy face, hands with missing or irregularly shaped digits, and from the waist down is essentially a spine that drags along the ground like a lazy tail as he crawls after you. Zephon is up there as well, being a vaguely arachnid creature, fused into the walls of a cathedral that was originally designed to be a superweapon to use against vampires, that produces eggs, in spite of originally being male. Rahab looks like an angler fish or a dragonfish that crossbred with a blue shark and grew arms.

And in the last Legacy of Kain game, you actually end up fighting Raziel, though you still switch between him and Kain. While you fight Raziel though, when he does one of the special attacks with the Soul Reaver, he looses the most insane, maniacal laughter that sends shivers down my spine.

Chrono Trigger is one that really ought to entertain you, especially with its deep storyline. The gameplay is dynamic, yet in many ways simple, and it's one where being able to go first is far more of an advantage than being able to do a huge amount of damage or sustain as much.

MOTHER series is a great one because of the sheer ludicrousness of it all, as well as the sheer horror of the endgame in all of them. All so much fun, but just try not to beat Earthbound before you go to bed. You'll keep seeing fetuses, twisted faces, and hearing, "It hurts, Ness..." every time you close your eyes.

To throw everyone for a loop, I recommend the Ultima series, in all its 8-bit or lower glory. Exodus is likely the one you'd be inclined to play the most at first, but I recommend that you play Ultima- A New Exodus instead, as it fixes many of the issues that were present in the original NES version of  the game. Also, I'd say it has what is potentially the greatest NES soundtrack ever. Quest of the Avatar is another good one, what with it focusing more on the fact that you're basically supposed to try making your character into some kind of saint instead of beat boss after boss. That both of them are very sandbox-y, especially for their time, really makes them shine through, though I will warn you, they can be hard as all Hell at the earlier levels.

Now that I think about it, Secret of Evermore is a great one as well, in spite of how linear it is. When you reach Ebon Keep in Gothica, you'll hardly be able to leave; the place itself, as well as the music, are so melancholy and beautiful that you won't even want to beat it.

For me, Imma be the odd one out and say the Soul series has been my favorite. The character design is always stunning in one way (drool-worthy like Ivy, Siegfried, Sophitia, and Z.W.E.I.) or another (Yoshimitsu, Tira, and Voldo for their garish or otherwise shockingly colorful costumes), and the scenery is almost so good that it's distracting. As well, it's an easy game to learn, a difficult and rewarding one to master, and, unlike many fighting games I've seen, has a decent storyline.

Timestalkers for the win.

I picked Daisy, but that's because I'd help her work up the nerve to act on her crush on Toadstool.