Last night, many AT&T wireless customers in South Florida had service trouble as some 3G and 4G networks went down. A switch in Broward County caused the issue, according to AT&T. But the slower 2G ("Edge") was still working.
Whenever you have service trouble, try the following:
1. Your settings may have a place to turn off the 3G network, so that it switches to the slower backup 2G network, known as Edge on AT&T. In the iPhone's settings menu, go to General > Network > Turn off Enable 3G (pictured here).
2. Just restart the phone. Sometimes a reset can help the phone reconnect with a working network, if it doesn't fix itself automatically or takes too long to switch to 2G. It worked for me late last night, bringing me back to full bars on 3G after getting a "No Service" message.