I am looking for a way to find out a unique_id for android device.
I will use the Id in login re
I think, you could use device serial ID (hardware serial number, not android id). You could seen it in device settings. In your code, you could get it by Build.SERIAL.
There is no such ID available on Android. You can generate your own, for example a random UUID and connect it to the user's account. This is what Kindle, Audible and other applications do to identify devices in a non-privacy-intrusive way.
Consider Google Analytics Mobile if you want to "track your users", http://www.google.com/analytics/mobile/
If you want to get closer to tracking a device you can combine the IDs above together in a hash-function. Bluetooth + wifi + android serial, and if any of them are null, you put a 0 in the hash, e.g. if there is no wifi mac addr. As you point out, you aren't guaranteed the id won't change. Unless the user is running a custom ROM, I would expect this computed ID to stay constant, though.
I have chosen to use Android_ID since It's not dependent on any hardware.
Build.SERIAL also dependent on availability of telephony that is in wifi only devices this Build.SERIAL won't work.
I have explained how other approaches are dependent upon the hardware availability in the question itself.