iMapIdle is an iPhone application that simulates “Push Email” with your IMAP server. It’s in its early stages but the current features are:

– listens in the background waiting for new IMAP mail even if you are in sleep/standby mode
– notifies you via a popup and/or sound. You choose how to be notified. Sound notification should use the same method your mail client uses (ie: if you have vibrate on, it’ll vibrate as well)
– popup notification allows you to choose whether the mail client should check for email right there by forcing the mail client to check the server (it doesn’t launch the mail client but just forces it to check the server). NOTE: Don’t choose this if you are in the mail client as it will exit (you’ve been warned). The popup will disappear after 20 seconds and if you miss it the iMapIdle icon will show you how many popup notifications you have missed
– supports SSL connections and special support for GMail IMAP

Notes:
– this has only been personally tested on 1.1.1. Reports are that it works under 1.0.2 as well
– have no idea at this point how it effects battery
– use at your own risk