This question have been asked already, but the answers seems still incomplete. The profound answers already found are the following:
But unfortunatly non of them could explain it with absolute certainty, why or why not an Android device has debug support, btw. I don't mean the debug flag in AndoridManifest.xml files.
To check whether or not a rooted device could be managed to enable debug mode, I've rooted my Samsung Galaxy with no luck, even the rooted Galaxy S is not debuggable.
How can I enable/disable the Debug-Mode on my Samsung device?!
Thank you!
Edit To clarify I look for a full debug enabled device, not the USB-debugging. Due to the stupid fact stackoverflow does not allow me to post images (low repuation score), this question has a little missunderstandig. I refer to full debug mode, shown in the Android Device Chooser column labeled Debug.
Edit2
For completeness of question I've added the screen shot image now.
All you need is to enable the USB debugging feature on your device.