How do I get an new email notification icon on the status bar of an iPod Touch? Is there a way to get a "new mail" notification on the status bar (that indicates the presence of unread email in the inbox) of my iPod Touch Model #MB528LL Version3.1.3(7E18).  

I see that the iPhone or other Apple handhelds are capable of an email notification in the statusbar as shown in the image:



I have not been able to find anything in the settings to turn this on, nor have I found an app that adds this functionality.
This is not built-in to iOS, but there are jailbreak tweaks like Notifier, OpenNotifier, et al. If you've jailbroken your device, try searching Cydia.

Once iOS 5 launches, it'll include notification center which consolidates notifications in an overlay that can be accessed by swiping down from the status bar, similar to Android, but still different from what you're asking about.