I keep my mobile data (2G/3G) always on, but when the screen turns off (standby), I want it to automatically get disabled. Turn the screen back on, and it should automatically enable itself. Is there a way to tell android to keep mobile data off while the device is in standby?
Yes. There are many applications available in Google Play Store.
The most powerful automation app is Tasker, which I use and recommend to others. You can also try battery saver applications like Juice defender, and Deep Sleep Battery Saver.
In Tasker, define the context as
If you are in need of more tasker profiles, go here.