mine always watch the news with us. I'd rahter they watched it with us, and we can explain anything they're worried about than leaving things to their imaginations (if you ever leave the house and walk past/into a shop selling newspapers they'll see the pictures on the papers and "wonder", not to mention the news they'll here on the radio while in shops/out and about).
I developed a phobia of escalators when I was younger (which lasted for just over 20yrs) because I "knew" about the Kings Cross fire, and "knew" that it started on an escalator - but didn't know the 'facts'. I just thought that every escalator was going to burst into flames, and this progressed onto getting my shoe/clothing stuck in it.
Mind you - I don't let them watch soaps as they're cr*p 