Andrew Fraknoi made a catalog with Astronomy applications for your mobile and you can found it here (most applications is for iPhone).
Now I going to leave here my modest list of Android applications:
The Google SkyMap let you observe the sky at night. To do that you must install the free application from Android Market. Open the application and point your mobile to the night sky, then you'll see in the mobile screen all the information about the star or other sky object that you are observing.
The Zenit Mobile Telescope is an application that isn't free and made almost the same task as Google SkyMap, it seems that has more information and best image resolution.
The eufisica is a free application with news about Physics and Astronomy. Is still at an early stage, but already has some downloads.
The NASA App is my favorite one. It's the official application from NASA and has news, APOD and other important information about Astronomy, Technology, Physics, etc. It's free. By doing a search in the Android Market you will find many NASA applications (some are official and free, others are not).
The Solar System Explorer Lite is a interactive 3D journey in the Solar System. It has planets, moons, asteroids and space probes.
The Exoplanet Explorer Lite is a journey to the deep space. It is based on latest available data. Explore 3D recreations in more than 500 known planets and systems.
