If you recently purchased the new and shiny 16GB iPhone, and you are in the habit of changing SIM cards, then the following is just for you. Apple has released a doc about swapping the SIM cards if after such operation your iPhone didn’t work.
Basically you need to reconnect your iPhone to iTunes. iPhone keeps a record of previously inserted SIM cards, but if the carrier name of your SIM does not show up in the status bar after you have changed the SIM you will need to reconnect iPhone to iTunes.
So remember for the next time that if you do not connect iPhone to iTunes after changing or reinserting the SIM, iPhone may not work as expected.