Over at 9to5Mac, Mark Gurman makes a good case for a resolution of 1704-by-960 in the iPhone 6. His unnamed sources say that Apple is in fact testing at least one model with this resolution, and he explains why this exact number of pixels makes sense.
If you took the original 3.5-inch iPhone with its 480-by-320 resolution and stretched it to 4 inches at the same pixel density, you'd have a resolution of 568-by-320. If you then tripled the number of pixels in each direction, you'd wind up at 1704-by-960. So while the iPhone 4, with its 960-by-640 resolution, was a "2X" display compared to previous models, the iPhone 6 will be a "3X" display.
Why does this matter? App developers will ultimately have to tweak their code to make things look great on the larger screen, but until that happens, it behooves Apple (and users) for these apps not to look horrible. An increase in resolution at the same aspect ratio would leave apps looking decent enough until developers got around to optimizing their apps. Unlike with the transition from the iPhone 4S to the iPhone 5, you wouldn't have to deal with any black bars surrounding the screen.
As for physical screen size, there have been reports of Apple testing a 5.5-inch iPhone as well. The rumor mill seems to agree that this extra-large iPhone won't arrive this fall, if it arrives at all. Either way, a resolution of 1704-by-960 would make for an increase in pixel density over current models and would allow Apple to take on the many larger Android phones that are already on the market.