Can I write native iPhone apps using Python?

It seems this is now something developers are allowed to do: the iOS Developer Agreement was changed yesterday and appears to have been ammended in a such a way as to make embedding a Python interpretter in your application legal:

SECTION 3.3.2 — INTERPRETERS

Old:

3.3.2 An Application may not itself install or launch other executable code by any means, including without limitation through the use of a plug-in architecture, calling other frameworks, other APIs or otherwise. Unless otherwise approved by Apple in writing, no interpreted code may be downloaded or used in an Application except for code that is interpreted and run by Apple’s Documented APIs and built-in interpreter(s). Notwithstanding the foregoing, with Apple’s prior written consent, an Application may use embedded interpreted code in a limited way if such use is solely for providing minor features or functionality that are consistent with the intended and advertised purpose of the Application.

New:

3.3.2 An Application may not download or install executable code. Interpreted code may only be used in an Application if all scripts, code and interpreters are packaged in the Application and not downloaded. The only exception to the foregoing is scripts and code downloaded and run by Apple’s built-in WebKit framework.

Not currently, currently the only languages available to access the iPhone SDK are C/C++, Objective C and Swift.

There is no technical reason why this could not change in the future but I wouldn't hold your breath for this happening in the short term.

That said, Objective-C and Swift really are not too scary...

2016 edit

Javascript with NativeScript framework is available to use now.

You can use PyObjC on the iPhone as well, due to the excellent work by Jay Freeman (saurik). See iPhone Applications in Python.

Note that this requires a jailbroken iPhone at the moment.