Olive Tree Bible Reader
http://www.olivetree.com/resources/free/
This is actually a Bible Reader for the iPhone. It also comes in Droid and Blackberry editions. It contains both the ASV and King James versions and it’s easily searchable. I whipped it out at a recent Bible Study session and found the verse we were discussing lickety split. Free.
Daily Ignatian Reflections
http://itunes.apple.com/us/app/daily-ignatian-reflections/id395830983?mt=8
If you are as big a fan of the Jesuits as I am, you will love this app. Every day you get a new reflection and prayer. Nice little anytime prayer break. Free
Busted Halo Mobile
http://www.bustedhalo.com/features/busted-halo-mobile
This isn’t an app, but it is a very good mobile stripped-down version of a very robust Catholic site. Busted Hero is geared mostly toward twenty-somethings, but I am double that age and learn plenty. As with any site, don’t read the comments or you will despair for the future of our civilization. Free.
Ooh Something Shiny! 
I need an iPhone.
I downloaded the bible (King James) to my Kindle. The search function isn’t fabulous, but I can usually get to where I need to fairly easily.
I am going to spend the rest of my evening reading through the Busted Halo site now.
Nice. I don’t agree with everything on Busted Halo, but I “get” even the parts I disagree with.