if they're using MSN messengert you can get it to save a copy of all their chat logs onto your hard drive. You need to open messenger and go to >tools>options>messages and select save a copy.
I think you'll need to sign in as the user (your kiddie) to set it up...
You could also install something like VNC/radmin (google them) which are remote control software, this would enable you to connect to the kid's pc from your pc and view their screen. You have an option to just view or to take control, but if you take control they'll realise that Big Brother is watching them, so just using the 'view' option would be best...
Hope this helps