Personally, I'm afraid of heights but heights never bothered me in games.
Put this on full screen and try not to go weak at the knees when you watch it.
http://www.youtube.com/watch?v=N93FpcvWGTo
The first time I watched this, I actually felt my knees start to weaken, especially when he looks down and you see exactly how far down it is.
As for Spiders, think of them as just pixels on a screen. They are not real. If it makes you feel less frightened, try to concentrate on the stupid noises they make and think how ridiculous it sounds.