Well glory be. Google has enabled push e-mail for the iPhone. Ever since we started using the iPhone, we wished for this, and in the meantime used GPush, which was off to a rocky start but now works perfectly. Anyway, now there's no third-party app necessary, because Google worked around Apple and modified Google Sync, working through the Microsoft Exchange account on the iPhone to bring your e-mail messages instantly.
Now, those e-mails are updated in the same way you could previously sync your calendar and contacts. No more waiting around for those messages to be pulled at preselected intervals, or manually checking your e-mail — hooray! There's one catch: You can only use one Exchange client at a time, so if you use Microsoft Exchange at work, you can't use Exchange for push Gmail.
Nice, Google. Now if you can just figure out how to work around Apple's mulish refusal to approve a Google Voice dialer for the iPhone, justice will be done. I'm hearing a few people say GPush is faster than push Gmail over the Microsoft Exchange client, so I'm thinking I'll stick with GPush for now. Let us know about your experiences and comparisons in the comments.