According to Apple's iPhone 3G specifications, iTunes 7.7 will be required to use the new device. Right now, the latest iTunes version available is 7.6.2.
With any iPhone or iPod update, typically, an iTunes upgrade is required too. This doesn't seem to be any different. It's unclear what features or functionality (on top of enabling new devices) will be included in the release.
In theory, iTunes should be released before the new iPhone hits store shelves on July 11, but Apple has not announced a specific release date for the software.
iTunes 7.7 will be available for both Mac and Windows.
Thanks to Beau, Fin, and everyone who sent this in!