said by ashrc4: Before recycling a phone, remove the SIM card. If you are not reusing the card, destroy it by breaking it in half. Delete any remaining personal information on your phone and restore the handset to its factory settings to fully erase the data.
One caveat here is that with some phones, the order of the quoted advice might need to be reversed. I have run across phones that would not let you get past a "please insert a valid SIM card" type of message until a readable SIM was installed.