Not all data in most cases, and not directly in others.
Of course, MobileMe will keep most of your contacts, calendars, mail and other "Apple"-supported things in sync. While it's not direct from iPhone to iPhone, for all intents and purposes, it appears that way -- make a change on one, and moments later, it appears on the other.
Some file storage apps have the ability to "share" files between themselves.
Yet other apps are meant to share contact information directly (over bluetooth or wifi) between phones.
If you're looking to do a "data dump" from one iPhone to another, I suggest backing up the iPhone with iTunes, then plugging in the 2nd phone and doing a "restore" from that backup.
What data, specifically, are you looking to migrate from one phone to another?