I like the Android platform. Actually, with some friends, we even participate in the ADC with the Spoxt project.
But Java is not my favourite language at all. We are working on an S60  version and this platform has a nice Python API. Of course there is nothing official about Python on Android, but since Jython  exists, is there a way to let the snake and the robot work together?
One way is to use Kivy :
Open source Python library for rapid development of applications that make use of innovative user interfaces, such as multi-touch apps.
Kivy runs on Linux, Windows, OS X, Android and iOS. You can run the same [python] code on all supported platforms.
There is also the new Android Scripting Environment  (ASE) project. It looks awesome, and it has some integration with native Android components. http://www.talkandroid.com/1225-android-scripting-environment/
An example via Matt Cutts  -- "here’s a barcode scanner written in six lines of Python code:
import android droid = android.Android() code = droid.scanBarcode() isbn = int(code['result']['SCAN_RESULT']) url = "http://books.google.com?q=%d" % isbn droid.startActivity('android.intent.action.VIEW', url)
"The Pygame Subset for Android  is a port of a subset of Pygame functionality to the Android platform. The goal of the project is to allow the creation of Android-specific games, and to ease the porting of games from PC-like platforms to Android."
The examples include a complete game packaged in an APK, which is pretty interesting. http://www.renpy.org/pygame/
There's also SL4A  written by a Google employee. http://code.google.com/p/android-scripting/
I've posted instructions and a patch for cross compiling Python 2.7.2 for Android, you can get it at my blog here: http://mdqinc.com/blog/2011/09/cross-compiling-python-for-android/
EDIT: I've open sourced Ignifuga , my 2D Game Engine, it's Python/SDL based and it cross compiles for Android. Even if you don't use it for games, you might get useful ideas from the code and the builder utility (named Schafer, after Tim...you know who). http://ignifuga.org
I just posted some directions for cross compiling Python 2.4.5 for Android . It takes some patching, and not all modules are supported, but the basics are there. http://www.damonkohler.com/2008/12/python-on-android.html
As a Python  lover and Android programmer, I am sad to say this is not really a good way to go. There are two problems.
One problem is that there is a lot more than just a programming language to the Android development tools. A lot of the Android graphics involve XML files to configure the display, similar to HTML. The built-in java objects are really integrated with this XML layout, and it's a lot easier than writing your own code to go from logic to bitmap.
The other problem is that the G1 (and probably other Android devices for the near future) are really not that fast. 200 MHz processors, and RAM is very limited. Even in Java you have to do a decent amount of rewriting-to-avoid-more-object-creation if you want to make your app perfectly smooth. Python is going to be too slow for a while still on mobile devices. http://en.wikipedia.org/wiki/Python_%28programming_language%29
SL4A  does what you want. You can install it on your droid easily from their site, and don't need root.
It supports a range of languages, Python support is currently for version 2.6, but there's a 3.2 port  you can use too. I've used that port for all sorts on a Galaxy S2 and it worked fine.
SL4A scripts have a library available for each supported language that gives you an interface to the Android API as a single
import android droid = android.Android() # say "hello world" using the text to speech facade droid.ttsSpeak('hello world')
var droid = new Android(); droid.ttsSpeak('hello from js');
There's also some support for native Android user interfaces.
There's also a third party project named QPython  that builds on SL4A, and throws in some stuff of their own. It has more features, and is actively developed.
Not at the moment and you would be lucky to get Jython to work soon. If you're planning to start your development now you would be better off with just sticking to Java for now on.
Using SL4A  (which has already been mentioned by itself in other answers) you can run  a full-blown web2py  instance (other python web frameworks  are likely candidates as well). SL4A doesn't allow you to do native UI components (buttons, scroll bars, and the like), but it does support WebViews . A WebView is basically nothing more than a striped down web browser pointed at a fixed address. I believe the native Gmail app uses a WebView instead of going the regular widget route.
This route would have some interesting features:
From the Python for android  site:
Python for android is a project to create your own Python distribution including the modules you want, and create an apk including python, libs, and your application.
I use the qpython app, it has a editor, a console, and you can run your python programs with it, the app is free, here is the link http://qpython.com/
Yet another attempt: https://code.google.com/p/android-python27/
This one embed directly the Python interpretter in your app apk.
There's also python-on-a-chip possibly running mosync:
You can learn sl4a Python Examples  http://code.google.com/p/android-scripting/
Didn't see this posted here, but you can do it with Pyside and Qt now that Qt works on Android thanks to Necessitas.
It seems like quite a kludge at the moment but could be a viable route eventually...
While there is one book called Developing Android on Android, of which introduce how to develop apps on the Android device by using the Python language, and this book should be a good start for you.