I have owned an iPhone for about a month now and I'm very happy with it. Its mail application is acceptable, but it's not very Gmail-esque. It does not have the conversation view, archiving e-mail means having to move it to "All mail", which is a bit annoying. Ergo, it works, but it's not perfect. The Gmail web application on the iPhone is very good, it works just like the desktop Gmail web client and it's fairly responsive for a web app, it's only missing one thing: the ability to check for new mails every x minutes. The iPhone mail app can do that, but of course, a web application cannot. Enter GPush (iTunes link). This $0.99 application enables push e-mail on your iPhone. You enter your Gmail credentials and whenever you receive a new e-mail, within seconds you will receive a push notification on your phone. You can then open a mail application (be it the native Mail client, or the Gmail web app) to actually read the e-mail. This may even save battery life, because your phone no longer has to poll for new e-mail every half hour, hour or whatever it's set to.
To test if the Gmail web app makes a good mail application replacement, I got rid of the native Mail application from my iPhone dock, and replaced it with a bookmark link to Gmail.
I'm not a privacy or security nut, but one concern is that you do have to give your Gmail credentials to the GPush service, which is maintaining an persistent connection to Gmail IMAP server through it. You hack the GPush service, you hack helluva lot of Gmail accounts.
Update: After a few hours of usage, GPush seems to have stopped pushing e-mail to my iPhone. Until that's fixed I found an alternative: PushMail. It works a bit differently and is not specific to Gmail. The idea is to automatically forward e-mail you want pushed to your phone to a special @dopushmail.com address. The nice thing about this is that you can create filters in Gmail to only push particular e-mails to your phone. I have been using it for a few minutes, and so far it's working. Let's keep our fingers crossed.