iPhone SDK and Free Software
This article pretty much sums it up. The iPhone SDK isn’t compatible with free software.
http://www.linux.com/feature/131752
So at this point it doesn’t appear to be possible to develop your own app under a (L)GPLv3 license, nor use any (L)GPLv3 code in the process. Of course the GPLv3 is fairly new, so quite a few open source projects are still under the GPLv2, but even in that case, releasing code that uses the iPhone SDK APIs may be violating the iPhone SDK license agreement.
In any case, the iPhone uses its fair share of open source software, including those projects maintained by Apple (http://www.opensource.apple.com/darwinsource/iPhone/) and quite a few more from the community, which are listed under the Settings -> General -> Legal menu on the iPhone itself. Strangely, I can’t find a version of that document online; http://images.apple.com/legal/sla/docs/iphone.pdf doesn’t seem to be the same thing. I’ll have to investigate this one further…
As for my own personal iPhone projects, they’ve been put on hold for lack of time right now, but the licensing conflicts are definitely making me question how much time I want to put into writing software that’s locked up, with only Apple holding the key.