I can proudly admit that I'm not an internet addict (luckily), so I could go without the Internet even all my life. :)
But I know that a lot of people are addicted by now and would have a huge problem without having access to the Internet.
I remember that I got mine when I was around 7 years old it was for my birthday and I think that around 8-9 is an adequate age to give your child a cell phone.