While no one should give out their home address or phone number in a public forum, it's important to face the reality that there can be greater risks than disclosing personal information.
Being an involved parent doesn't necessarily mean standing over your kids shoulder when they go online, but it does mean talking with them about their Internet activities.
For some reason, the moment anyone mentions the word "computer" or the "Internet," everyone panics. I don't know why. All the normal advice about using common sense to stay safe applies exactly the same in cyberspace.