*3001#12345#* and tap Call. Enter Field Mode.Field mode reveals many of the inner settings of your iPhone, specifically up-to-date network and cell information.
*#06# Displays your IMEI. No need to tap Call.
IMEI is the unique identifier for your cell phone hardware. Together with your SIM information it identifies you to the provider network.
*777# and tap Call. Account balance for prepaid iPhone.
*225# and tap Call. Bill Balance. (Postpaid only)
*646# and tap Call. Check minutes. (Postpaid only)
These three are pretty self explanatory.
*#21# and tap Call. Setting interrogation for call forwards.
*#61# and tap Call. Check the number for unanswered calls.
Show the number for voice call forwarding when a call is unanswered. Also show the options for data, fax, sms, sync, async, packet access and pad access.
*#62# and tap Call. Check the number for call forwarding if no service is available.
Just like the previous, except for no-service rather than no-answer situations.