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Here is a list of the Catholic apps that I currently have on my new iPod Touch. I found all of these through the iTunes Apps store by searching on the word "Catholic". These are all free. I believe they are all faithful to the teachings of the Roman Catholic Church; they certainly enrich my faith journey! The titles listed below match the titles in iTunes.
Catholic Bible: Yes, the entire Bible!
Catholic Mass Times Church Directory: Awesome! Easily shows the Catholic churches closest to my location with a link to addresses, maps and Mass times.
Divine Mercy Guide: Steps me through the Divine Mercy chaplet, etc.
Evangelizo -- Daily Gospel: Terrific! Automatically loads the Mass readings for the day, and has other prayers for the season.
The Holy Rosary: Nice aid to prayer.
iCatholicRadio - The Station of the Cross: Indispensable! Easy access to 101.7 FM (Buffalo): livestream their radio broadcasts and get their podcasts, etc.
The Lord's Prayer: Meditative music to listen to while contemplating the prayer that Jesus taught us.
Night Prayer, Compline -- FREE Audio Liturgy of the Hours by DivineOffice.org: Automatically downloads the Liturgy of the Hours for the day, the night prayer.
Rosary - Mysteries of the Holy Rosary: Nice prayer aid.
iBooks (this is general app for reading any book, but I downloaded from the Gutenberg Project an ePub format file of Thomas Aquinas' Summa Theologica)
Upon googling Evangelizo to get the art for this blog post, I see that Evangelizo is also available for the Android, and that is probably true for others.