One possibility is
Prowl, which is an iOS implementation of the
Growl notification system.
The app costs a few bucks, but you get a free
ProwlMail account. Anything which gets sent to that account (say, automatically forwarded copies of your email) will show up as a full-on iOS notification (just like a text message, vibration included if you want).
The configuration is a bit of a hassle, but it's not because there's anything wrong with it, it's just insanely powerful.