UPDATE OCT. 2011 - The question has been answered. As of the release of the iPhone 4S, Oct. 14, 2011, Sprint is offering the iPhone.
Unlike a T-Mobile iPhone, which requires some technology changes, putting the iPhone on Sprint won't require any technology changes to the iPhone, making it more likely to happen soon.
Verizon and Sprint use the same kind of CDMA network for their phones. When Apple brought the iPhone to Verizon, it had to create an iPhone with CDMA-compatible chips in it. With that kind of iPhone now in existence, there don't seem to be any technical barriers to a Spint iPhone. The major barrier would seem to be a business one.
While the iPhone isn't exclusive to any carrier anymore, it seems reasonable that Verizon might have negotiated some period of time that it would sell the iPhone before another competitor could enter the market. That's just an assumption, though, and no details about this have been made public.
iPhone on Sprint Release Date
Neither Apple nor Sprint have made any public statements about bringing the iPhone to Sprint, so any release-date discussion is speculative right now.
That said, speculation is growing strong that Sprint will be one of the carriers of the new iPhone 5 when it debuts in the fall of 2011. There's no single piece of evidence pointing to this, but a tremendous number of rumors and signals indicate it. Expect it to happen.
Last Updated: Oct. 4, 2011