Developing Android apps the fast way! App Inventor allows you to plug together building blocks to quickly create apps for Android phones.
Visit MIT's App Inventor set-up instructions for instructions to prepare your computer to run App Inventor. App Inventor is a web-based tool for layout of the app, with a Java 'block editor' application to help you design the logic via plugging blocks together.
You will need a PC (or Mac), with Java JRE 1.6 or above installed, and ideally an Android phone with a USB cable, but you can use the emulator to test your projects.
MIT's tutorials are well worth using as a starting point.
App Inventor main website has many other resources on it.
App Inventor tutorials and resources hosted by Google. Note you can download more or less the complete text of the book “App Inventor”, by David Wolber, Hal Abelson, Ellen Spertus and Liz Looney here.
Web database examples using Google App Engine - also look at the other examples on the right hand side, if you want to run your own engine on your website.
Here are some files you can download to have a play with.
Simple two screen example. Note you cannot test multi-screen examples on your phone directly, you need to use 'Package for Phone' and 'Download to Connected Phone' in the top right hand corner.
Advanced example faking tabbed display (there is no tabbed control in App Inventor) - Cats from Wikipedia (GPL/CC license).
AppMan. Advanced example similar to an old favourite. This is a game still in progress, but shows the use of timers for managing animation, and controlling a sprite using on screen buttons.
Simple spirit level app, with calibration.