Perhaps the most impressive Christian iPhone and iPod Touch applications are bible study applications available through the iTunes store. The big advantage they have over website based bible study tools is that often you can access them offline no matter whether you have a 3G of wireless connection. This also means that searching and reading the bibles is quicker.
Of course this means that you will need some spare space on your iPhone or iPod Touch, but generally this will not be huge compared to the other media you will have. The other disadvantage currently is that the variety of bible translaions available is not as large as web based applications.
A well designed iPhone application with multiple translations both online and offline and regular updates.
ESV bible (via Kindle)
A free ESV bible on your iPhone, if you live in the US…
Holy Bible by Paul Avery
A good selection of free bibles with note taking and bookmarking included.
Bible Reader (Olive Tree)
An easy to use offline iPhone bible that would benefit from additional translations
CCEL iPhone bible
2 free bibles and 3 books on your iPhone (more books on the way!)
Mantis Bible Study
A very well designed bible package for the iPhone, but with only the KJV provided free with the application
Sword Drill 2
This is a relatively easy way to access the Bible Gateway website. However you need to be online for it to work.