When Apple initially announced the iPhone SDK, there was much dismay over the lack of background process capabilities, which disallows third-party applications to, for instance, notify the user of incoming instant messages or other network operations.
The company is now addressing this situation with what it calls a robust push architecture available to all third-party apps. This is an Apple-owned server that developers can access and use to push notifications to iPhone users.
Regarding the use of background processes, Apple's documentation still says:
"Only one iPhone application can run at a time, and third-party applications never run in the background. This means that when users switch to another application, answer the phone, or check their email, the application they are using quits."