Your children could be your biggest security risk if you're not vigilant. Make sure you lock down every internet-connected device they can get their hands on. Pre-teens and older will need their own profiles, and you should still keep track of their access, check browser histories and look for modified files on your computer. Use different passwords or use an app to generate complex passwords, and make sure every purchase requires a password. Use a duplicate backup system.
Children are also a big target for identity thieves (sometimes within their own family). Signs of fraudulent activity include offers of credit mailed to the child or identity issues when applying for schools. It is not recommended that you monitor your child's credit report annually, as that can actually create a file prematurely. Check only if you see red flags, or at age 16 before applying for college and financial aid. Click here for more information from the ID Theft Resource Center.
Bottom line: teach your children continuously about the importance of protecting their privacy online and the dangers of identity theft.