Here are some resources which you can learn Mobile Application Programming in iOS and Android:-
1. CS 193P iPhone Application Development Free Video Courses by Stanford University (Self Learning)
For your information, Professor Paul Hegarty is a good friend of Steve Jobs and he has worked for Steve for 8 years in NeXT Computer. Eventually, Next Computer was acquired by Apple and the foundation of OS X and iOS operating systems is built based on NeXT. If you only have to choose only one source to learn to program in iOS, I would highly recommend this free lecture by Professor Paul. Professor Paul understands the Apple technology really well and his lecture is easy to understand. His lecture also updates regularly based on the current released version of iOS. You can download all the videos tutorial from iTunes University
Source: CS 193P iPhone Application Development
2. Apple WWDC 2013 Videos
Is there any better way to learn iOS from the apple engineers themselves? The Apple Worldwide Developers Conference (WWDC) is held yearly and the engineers show us the best practices and also the latest framework development in iOS. You will have to master the basics in your area of interest in iOS programming in order to understand these videos. You will need to be a registered developer to access to these videos.
Source: Apple WWDC 2013 Videos
1. Free Android Application Development Video Course by The New Boston
I believe The New Boston has one of the best free android development tutorial on the Internet. One drawback I found out is that the course is not updated based on the latest version of Android SDK. The tutorial is taught using Android 2.2.x (API Level 8) as the targeted version with older version of Android Development IDE (Eclipse).
As of July 2013, the latest version of Android is 4.2.2 with API Level 17. If you are watching the tutorial, you might find some of the configurations/steps can not be followed. So, you will have to find the ways yourself.
Source: Free Android Application Development Video Course (The New Boston)
2. Android Development Training
If you want to learn the latest Android SDK, the best resource (without any doubt), is the training by Android itself. But, there isn’t many video tutorials there. So, you will have to read through all the resources.
Source: Training for Android Developers