I'm happy to have spiders in my house, though I don't like their webs which hold the dust, and I wouldn't touch a very big spider. I never kill anything if I can avoid it, though I have killed mice as I can't have them running around the house!
You can de-sensitise yourself. I used to be scared of daddy-long-legs but when my kids were born I decided that I didn't want to pass my irrational fears onto them, so I gradually forced myself to stay in the same room as one, and now I can pick one up. My kids, I'm pleased to say, aren't frightened of anything, even if they may not be overkeen on handling a creepy-crawly. My daughter is better than my son actually!