The next-generation iPhone will launch on September 6th, according to German Apple website iFun [Google Translate]. The site does not have a significant track record with this sort of prediction, however.
Earlier this week, KGI Securities analyst Ming-Chi Kuo said the low-cost iPhone and the iPad 5 would ship in early September with the iPhone 5S coming later because of production difficulties. Kuo has had an excellent track record in recent years. A ramp in production of the iPhone 5S at the end of this month was reported by a number of parties last week.
Rendered mockup of lower-cost plastic iPhone front and back
Additionally, iFun claims two new "device types" will be introduced, likely an iPhone 5S and a new low-cost iPhone with a plastic backing that has been extensively rumored.
During Apple's earnings call this week, CFO Peter Oppenheimer said that Apple would have a "very busy fall" and said he would go into more detail "in October". It isn't clear whether he meant because new products would be launching then or because that's when the next earnings call will take place.