At last here is the official Indian Railway Catering and Tourism Corporation application for the android devices named IRCTC connect.
The application is really easy to use. It will help you find and book trains.
Features
You can login with your existing IRCTC login ID or password or can create a new user id from App directly
Easy to Search, Find and Book train tickets
View booked tickets and Cancel tickets
Retains recently added passenger details
Upcoming Journey Alerts
You can get this application from Google Play store
It is requested that you read the comments from the users who used the application. They says there are many issues with this application. We believe that the application is on the initial state so it will be improving in the future. Read one comment from Abjijeet Kharparde
Good But Not Satisfactory: 1st issue, does not remember the login details even though ticked to remember. 2nd issue, not synchronize with website, not shows the booking done through website & the major issue, do not allow to do transactions from 8.00 AM to 12.00 AM, not getting why such policy by Indian Railways Need to improve a lot.
The 8.00 AM to 12 .00 AM restriction seems to be a big problem, hope they will resolve it fast.