Google's Videos app, the official video player for Android Market movie rentals, has been updated to work on Android smartphones. The app was previously, only supported on Android 3.0 (Honeycomb) tablet operating system. The latest update, however, only support those smartphone running: Android 2.2 (Froyo) and Android 2.3 (Gingerbread).
"Select from thousands of movie titles in Android Market and begin watching instantly -- no wires, no syncing, no hassle! Make your movie rentals available for offline use on your supported Android device so you can watch even when you're not connected. Also get quick access to your personal video collection, including those you've taken yourself using your phone or tablet camera," read the app description.
Once the app is installed on your Android phone, you will have access to both your own rentals from the Android Market as well as any personal videos stored on your phone. In my case, as I don't currently have any rentals on my device, the "My Rentals" section included a list of "Top Rentals" instead.
It appears that this app is designed to work with the updated version of the Android Market. When you're in Google Video, a tap on the small Market icon on the top right on the main screen automatically opens up the Movies section within the full Android Market app, assuming you have the newest version.
You can download the free Videos Apps from Android Market.
Table interface screens: