When you set-up Gmail on your iPhone you've probably noticed that that are not automatically pushed to your phone, you manually have to go into the Mail App to check for new Mail all the time.
It is possible however to have Gmail pushed to your iPhone - Just be warned if you get lots of Spam or if you're particularly popular the constant beeping every time you get a new mail could get rather annoying :-)
Here's how to set this up:
1. Choose Settings from your iPhone Home Screen
2. Choose Mail, Contacts, Calendars
3. Choose Add Account
4. From the screen that appears tap Microsoft Exchange
5. Under Username, enter your full Gmail address
6. Under Password, type your Gmail password
7. Under description you can type a name, for easy reference you could put 'Gmail' and press Next
8. Type m.google.com as the server and choose next
9. Press the switch to turn Mail On, you can also turn on Calendars if you wish to sync your Google Calendar and Contacts should you wish to sync your contacts - This option is particularly useful if you have migrated from an Android Phone, you can access all of your contacts without having to copy them over.
10. Press Done
Voilà! You now have push Gmail on your iPhone!