I would like a local notification to be fired when a call is received (and to show an alert) - is this possible? Can a call event get an app to launch or a notification to b
If your application is running while a call is in place check out the CoreTelephony Framework. The CTCall class provides information about the call state. I have not used this myself but you may find it useful.
extern NSString const *CTCallStateDialing;
extern NSString const *CTCallStateIncoming;
extern NSString const *CTCallStateConnected;
extern NSString const *CTCallStateDisconnected;
Edit:
The CTCallCenter allows you to register for call event state changes. As I said before your application will need to be running to know that something has changed. You may want to request the maximum backgrounding time (I think it is 10 minutes now) when your application is moved to the background. These api's are only available in iOS 4.0 and later.