I close my eyes in Pirates of the Caribbean with the skeletons, which just creeps me out.
I close my eyes at the beginning of Big Thunder Mountain because of the bats.
I haven't been on Snow White since 2000, because the ride scared.
I won't go on Haunted Mansion, because scary things (even creepy, fun things) scare me...
I close my eyes on Expedition Everest before the Yeti animatronic appears. Strangely, I don't mind the Yeti, ever since I started lurking on the WDWMagic forum, and a few guys have it as their avatar. I'm just not ready for the real thing... Also, their pictures are tiny, so that's another factor

I close my eyes in Great Movie Ride during the Alien scene.
I will never ever EVER ride Dinosaur... EVER!!!
I don't remember what Honey I Shrunk The Audience is like, because I never got to see it again. I just remember it being scary...
I cover my eyes on most roller-coasters because the noise is so loud!
I won't go on Rock n Roller Coaster because of the beginning (I went on last trip to please my parents, and it just reminded me why I avoid it...)
I won't go on Tower of Terror because I hate free-fall rides.
I don't look up just before the drop on Splash Mountain because of those vultures. They're so freaky!
I won't go near Universe of Energy, due to dinosaurs. Once was enough, and I spent it with my eyes closed...
I "close" my eyes on the Finding Nemo ride when that angler fish appears (closed at first, then squinting to see it, because I don't know...)
Uhm... I won't go near the T-Rex Cafe, because of dinosaurs.
Hmm... I can't think of anything else that creeps me out in WDW atm...