Hi,
I posted a thread on emoze some time ago.

Emoze was a free push service that you can use with gmail, gmail apps, using their servers or any other email using an always on computer with outlook.

Now you have consilient
Free Mobile Push Email - Consilient Push
free push again, but this time even for imap and pop, so zimbra :-)

It supports most of the phones. Mine not very well though (htc p3300 with wm6 touch).

I never heard about this french guy with his funambol and zimbra....

I have the feeling that push free services are going to pop up from everywhere, nevertheless as a Open Source user that does not want to go for a hosted zimbra, it is a petty that I cannot install a layer in my server to push email myself...