The Islamic Anasheed app offers a collection of the best Islamic nachid.
You will find songs in praise of the Prophet Muhammad or Allah and religious songs in different tunes without any musical instrument, or percussion instruments.
All songs of this application will be read directly from the Internet (requires wifi or 3G connection). However, there is an option to download any song you like Islamic and have it on your phone and then listen to it when you do not have Internet (offline).
Anashid also allows a customizable list of your favorite tracks.