Not all these codes can be applied depending on the service you use.
Field Mode
*3001#12345#* and tap
Field mode is inner settings of your iPhone, specifically up-to-date network and cell information.
IMEI
*#06# Displays your IMEI, like the other phone
IMEI is the unique identifier for your cell phone hardware. Together with your SIM information it identifies you to the provider network.
Account balance
*777# and tap
. Account balance for prepaid iPhone.
Bill Balance
*225# and tap
. Bill Balance. (Postpaid only)
Check minutes
*646# and tap
. Check minutes. (Postpaid only)
Call Forwards
*#21# and tap
. Setting interrogation for call forwards.
Discover the settings for your call forwarding. You'll see whether you have voice, data, fax, sms, sync, async, packet access, and pad access call forwarding enabled or disabled.
Calling line presentation
*#30# and tap
. Calling line presentation check.
This displays whether you have enabled or disabled the presentation of the calling line, presumably the number of the party placing the call.
Check the connected line presentation
*#76# and tap
. Check whether the connected line presentation is enabled or not.
State whether the connected line presentation is enabled or disabled. Presumably similar to the calling line presentation.
Call Waiting
*#43# and tap
. Determine if call waiting is enabled.
Displays call waiting status for voice, data, fax, sms, sync data, async data, packet access and pad access. Each item is either enabled or disabled.
Check the number for unanswered calls
*#61# and tap
.
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.
Call Forwarding
*#62# and tap
. Check the number for call forwarding if no service is available.
Just like the previous, except for no-service rather than no-answer situations.
Call Forwarding when busy
*#67# and tap
. Check the number for call forwarding when the iPhone is busy.
And again, but for when the iPhone is busy.
Call Control bars
*#33# and tap
. Check for call control bars.
Check all the usual suspects (voice, data, fax, sms, etc) to see whether barring is enabled or disabled for outgoing.