Apple's MobileMe services are working for most, though there are still sporadic reports of misbehavior. One point of contention, however, has been the exact behavior of their advertised "Push" services.
At the moment, the Mac OS X updater for MobileMe is available only for Leopard, and Tiger users will continue to use their ".Mac" control panels. In order to use the advanced Push capabilities of MobileMe from your Mac, you need to enable "Automatic" synchronization by selecting it in the MobileMe control panel:

Doing so will allow updates from your iPhone and Me.com to be pushed to your Mac near-instantaneously. Similarly, push services also work from many other combinations for Calendar and Address Book data. (The Mac OS X mail client remains sync only):
Changes to Me.com -> Mac (push)
Changes to Me.com -> iPhone push)
Changes to iPhone -> Me.com (push)
The point of contention comes when changes are performed on your Mac. These changes do not trigger an automatic sync and instead waits until the next scheduled sync which is every 15 minutes:
Changes to Mac -> Me.com (15 minute sync)
Apple has confirmed that this is expected behavior in a Knowledgebase article which has generated some complaints in our MobileMe forums. Alternatively, users can hit the "Sync" menu option at any time on their Mac to trigger a sync at any time.