IPhone Push Notifications for any IMAP account
msgpush.com
msgpush.com
You'd never give your password to someone if they asked you in person, but if it's a website, that's a whole different scenario.
Many people will give their password to anyone who asks, and most will give their password to someone who offers them a candy bar.
(I do have a separate MobileMe e-mail account account as well. Perhaps it changes the IMAP intervals system wide?)
We just have to wait till Google implements push for Gmail.
I say far as I can tell, because during the registration, when I saw they were asking for password instead of using SSO, I abandoned.
"Information collected may include: contact information such as your name, phone/cell numbers (during the course of technical support incidences), e-mail address(es), e-mail password(s) (to monitor your mail account for new messages), an identifying question for security check purposes, billing information (if you choose to join our service post Beta) and information related to those of our service(s) in which you have expressed an interest."
These is a background notification service any iPhone app can use that can show a text message on the screen and update a counter (aka "badge") on the icon of an app that isn't running.
Push notification in iPhone OS 3.x is not to be confused with Exchange or ActiveSync so-called Push email.