Android: Parents often want their kids to have mobiles for security reasons, but don't want them used constantly. Guardian is a free app that lets you set usage limits on who your kids can contact, which apps they can run and the times when they can use the phone.
You can set Guardian to block specific apps, or only allow them to be run at certain times of day. You can also control texting and web access the same way. Calls from numbers not on the phone's contact list can be blocked. An emergency mode lets the phone be used for calls when the phone is locked, but automatically notifies a parent via text when this happens.
While Guardian is developed by Vodafone, it can be used on any network. (The main visible Vodafone component is that Vodafone customer service numbers are automatically included on the "always allowed" list.)
Guardian is a free download from Google Play. If you try it out, tell us your experience in the comments.