Sparrow for iOS
itunes.apple.com
itunes.apple.com
I'm sorry but this is 2012. We've had push email for over a decade (perhaps slightly less than that on mobile phones? not sure of the exact figure). In today's world, not being constantly connected is a big deal.
Looks nice though and I understand that, due to iOS limitations, it's a bit difficult to provide push notifications for certain types of services (as they outline, they really would have to store your credentials server-side to do it); I just don't see the rational here.