Actually the best thing to do is educate your kids that there are some bad people out there, there's an awful lot of people who talk bollocks, and that they shouldn't consider meeting any of them in real life.
After that just leave them the hell alone, if you've done your job in bringing them up being capable of rational thought, and not just turned them into a braindead dribbling vegetable who requires mummy to bubble wrap him before he's even allowed to go anywhere near the front door he'll be fine.
I had internet access since I was 12, and despite any array of messed up videos, pictures, and stories having passed my eyes it hasn't stopped me achieving well over the average in life in terms of education, career, house, and a nice family.
Really, kids don't need protecting, they just need educating about the dangers of the real world, rather than simply shielding them from it so that if they eventually do encounter something, they don't know what to do. It's the same with many things in life - the ones who start binge drinking when they hit 16 - 18 are the ones whose parents told them that alcohol was the source of all evil, rather than the ones who were allowed a bit of alcohol each new years eve and taught to enjoy it, but not to have too much.
Keeping kids naive is the real problem, as long as you've taught them to be aware of the things that can really get them in trouble, like paedophiles, then contrary to The Daily Mail and so forth, no amount of porn, or nasty videos will turn them into a psychotic murderer - the only thing that'll do that is bad genetics, or a truly violent and abusive upbringing - at that point the internet is already the absolute least of your worries.
Oh, and for those parents who'll inevitably tell me I'm wrong, and that little timmy needs to be sat behind a filter for his own good - here's some news for you, little Timmy already knows how to get round your filter, and if he doesn't, he knows how to get round the school's filter, and if he doesn't know that, he'll know someone with uncensored internet who he'll visit, or other kids will bring print outs or copies of content you don't want them to see into school on their phones and so forth. Either way, little Timmy will find a way to see it regardless.