According to the Free Dictionary, the definition of cyborg is:
cyborg (cy·borg) n. A human who has certain physiological processes aided or controlled by mechanical or electronic devices.
Arguably, by this definition, any grandparent with a pacemaker is a cyborg.
Yet the connotation of cyborg is clearly something more invasive feeling than that. It is of a half human, half machine. That has never seemed like a very good definition to me, because the human body is itself a machine, composed partially of organic parts (ie, carbon compounds). Yet there has clearly been a significant divide between organic machines and non-organic machines.
The organic vs. non-organic divide is often confused with a natural vs. synthetic divide. But in a world where organic parts are rapidly becoming synthesizable, that distinction may eventually fade.
The clearer separation is between organic parts (flesh, plant matter) and non-organic parts (plastics, metals, etc.), and the separation between organic parts (brains) and non-organic parts (chips).
Those divides have recently shrunk:
Organic parts (flesh) can now be interfaced with non-organic parts (plastics, metal) seemlessly. Researchers at University College London, studying how antlers interface with flesh and skin, have created prosthesis that bond with flesh (see http://news.bbc.co.uk/2/hi/health/5140090.stm).
Organic parts (brains) can also now be better interfaced with non-organic parts (chips). As the journal Nature reports, researchers at Brown University have developed a system that improves the previous state of the art of technology that allows a paralyzed man to move a computer cursor, open e-mail and control a robotic device simply by thinking in a particular way about doing it (see http://www.msnbc.msn.com/id/13830825/).