Gizmodo cites unnamed sources that the new iPhone 2.0 firmware will be ready this Friday entering golden master stage.

Current iPhone owners can upgrade to firmware 2.0 for free. iPod touch users have to pay 10 bucks to get it (not sure why Apple considers it necessary to milk iPod touch owners).
The rumored Friday date does not necessarily mean Apple will release the new iPhone firmware. I think Apple will wait at least until Monday.
The iPhone 3G will ship on July 11th. The new firmware can of course be released before that date.
More details on Gizmodo.