Whether you're a follower of a religious faith, interested in them or just interested in the texts themselves, there's no shortage of Apps that revolve around religious writings.
Christianity

There's a lot of Bibles in the App store. A whole lot. LifeChurch.tv's simply named "Bible" (Free) -- presumably they got into the App store before the others -- offers the Christian Bible in a variety of translations, from standard stuff like the NIV or King James to slightly more obscure translations such as the 1934 Vietnamese Bible, either streamed over your wireless or 3G connection, or downloaded for selected translations.
Islam

The Qu'ran's less populated in the iPhone App store than the Bible, but there's still some good resources within. alQuran (Free) offers up the Islamic holy text in a variety of translations, including Arabic for native readers and 30 other languages. iQuran Pro ($13.99) offers a variety of translations and recitals of verses from a variety of speakers.
Judaism

The Torah Bible Pentateuch (free) offers up the Torah for free, but only in Hebrew. iTorah ($19.99) offers translations, commentaries and audio lectures, and the similarly pricey iTalmud English Edition $29.99 offers the Talmud with many of the same style of features.
Hinduism

The diversity of Hindu texts does make it rather tricky to pick a single App that represents the faith, and there's not too many to choose from in any case. Jumpn Crew offers the Vachanamrut (Free), the Swaminarayan Hindu scripture, while AartiMantra ($4.99) offers more than thirty prayers grouped by Hindu deity. Echoes Of Ancient Indian Wisdom ($3.99) isn't so much an App as a book, and it notes that even it just captures "a few echoes" of the Hindu faith.
Sikhism

In an age when the "i" appelation gets added to everything, it's surprising not to find more religious text applications using it. iSikhi quite obviously does, and offers searches of Sri Guru Granth Sahib Ji, Gurdaas Ji's Vaar and Dasam Granth.
Taoism

Daily Tao ($2.49) gives a daily quote from the Tao Te Ching with nature backdrops. It's more of a contemplative tool than a religious study text, for what that's worth.
Buddhism

We couldn't find the Tripitaka directly on the App store -- the only faith that we found with nothing searchable if you discount Scientology -- but Buddha Quotes ($1.19) uses a shake interface to present randomly picked sayings of the Buddha, while Buddhism: Question And Answer.
Baha'i

Bahâ'î Faith (Free) describes itself as the "perfect companion" to the Bahâ'î Faith, including writings, teachings and an introduction to the faith itself.
Also in this series, Amazing apps for your phone:
Part 10: Let the music play!
Part 9: 6 of the best augmented reality apps
Part 8: Tick Tock, Tick Tock - Ten Time Telling Apps
Part 7: Score a shopping bargain
Part 6: Photography apps
Part 5: Get from A to B on public transport
Part 4: What's the weather like out there?
Part 3: Top 3 twitter clients for iPhone
Part 2: Here's how to get cheap iPhone apps
Part 1: How to make the most out of your iPhone's GPS
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