Apple announced the new online service MobileMe at the WWDC 08. The .Mac replacing service is already available for pre-order on the Apple Store and apparently for some existing .Mac customers their new @me.com email addresses started to work.

According to MacRumors not all .Mac users are able to use their new me.com email address yet.
.Mac users will be able to keep their old @mac.com addresses, but also can use the new @me.com one.

The Me.com site is still now live. MobileMe is expected to launch in July - possibly on July 11th together with the sales start of the iPhone 3G.

MobileMe automatically pushes new email, contacts, and calendar events to your Mac or PC and over the air to your iPhone and iPod touch. So no matter where you are, your devices are always up to date. You also get easy photo sharing and 20GB of online storage.

The yearly subscription price is $99. If you buy any new Mac you get $30 off from your first year MobileMe subscription.
More details on the Apple Store.