OK, here's how..
For each affected user..
System Preferences » Accounts » Login Items
adjust to taste.
Skype installs itself like that, so it might not be the kids' fault.
Also, it might be very easy to select "Open at Login" when you right-click
on the icon in the dock, even by accident. And, I just did some random
testing, and it seems just as easy to turn "Open at Login" off via the
right-click on the dock app icon. No need to bother with Sys Prefs.
Is the right-click to "Open at Login" new in some Tiger update? I feel like
I just saw it on a tip, but I don't pay much attention to those menus.
Daiya