[untog]

As for iOS client's there are exactly 3 that come to mind. Gmail, Apple Mail and Sparrow (discontinued).

There's a good reason for that- Apple won't let you check a mail server on the client side. So you have to do what Mailbox did and set up huge server infrastructure to check people's e-mail then send push notifications. It makes it a lot more difficult than just making a client app.

[e12e]

So, the "solution" is to have your users set up a .forward-filter that pings a web service on new mail? Then have a really simple status server that simply replies with number of new mails since last check (or something along those lines...) - and have your email client poll (and reset) that counter... would give a few false-positives, but probably be better than having to poll an actual (variety of) IMAP/POP3-servers.

(This obviously won't work for most end-users, sadly)

[eaigner]

Yes, but we run our own servers.