They don't bother me at all, I'm happy to pick them up and pop them out in the garden where they carry on doing their spidery job (I imagine in my Pollyanna way that they reduce the numbers of vile flies and other bugs around.)
HOWEVER, my daughter (17) is quite severely spider-phobic (just goes to show it's nature not nurture) and I have a close male friend whose life has been somewhat limited by the same thing. Both of them are genuinely disturbed even to see a photograph of a spider, and one in the room can unsettle them for hours after it's been got rid of.
My attempts to convince DD from an early age that they are harmless have all failed, I used to 'personalise' the spiders, giving them names, making her look at them from afar while safely contained, etc, but none of it worked. My male friend, who lives alone, has only learned to cope by having a suction device to hand at all times to remove them, and not just any old device either, it must be one where no contact at all with the little beastie is guaranteed in the disposal thereof.
Phobias aren't, by their very nature, rational, and thus difficult to treat by using reason, but one tip that male friend gave me to try to help daughter (who goes off to Uni soon and thus no more midnight calls to Mum to deal with rampant spider in room) is that she should begin by drawing something vaguely spider-like until she can look at it without fear, then progressing to increasingly realistic pictures. Also, that once she's comfortable with that, to stare for 30 mins at said picture, because fear is a measurable physiological reaction which the body can't sustain beyond a certain point - boredom WILL set in sooner or later as you stare fixedly at even a disturbing image.
But there are all degrees of phobia and not many people are this badly affected.