When you launch Safari or other applications that need an Internet connection, the iPhone checks if the wi-fi is on and if it can connect to a network; if it can't, it automatically uses EDGE. If you don't have a flat data plan on your SIM card, this could easily consume all your credit!

To permanently disable EDGE, go to Settings / General / Network / EDGE, and type a wrong value for the APN setting; this way the iPhone won't be able to connect to a valid EDGE connection.

If you want to disable EDGE just temporarily, and be able to easily re-enable it at any time, download Boss Prefs through the Installer application, then launch the new application and use the switch to enable/disable it.