How can I tell my Cocoa application to quit from within the application itself?

You can pretty much rest assured that your app is going to get killed at least some of the time. Thus, defending against exits the like of exit(0); is required.

However, NSApplication implements the -terminate: method.

[NSApp terminate: nil]; ought to do what you want.

I would generally suggest posting it via -performSelector:afterDelay: with a delay of 0.0 to force it to happen at the top of the next pass through the event loop.

Example:

[NSApp performSelector:@selector(terminate:) withObject:nil afterDelay:0.0];