While there is no question that some amount of identity theft and other unsafe practices occur over the internet on a daily basis, the internet is largely a very safe place. By the numbers, only a very small percentage of people engaging in internet commerce, and most transactions are very safe.
The Internet can be a wonderful place to network with other people who have similar interests, or with family and friends who are far away. But it should never be considered to be a safe place, and one's guard should never be down, especially when children are allowed online. There is far too much anonymity on the 'net. People can pretend to be someone totally different, and children can especially be taken in by this type of ruse.