Doc has lost track of the time spent travelling; for him there has never really been any true measurement of time. With his ability to travel through time he has become less focused upon timelines and more fixated upon experiences and events. 

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Just like his human counterparts, Doc uses a TARDIS for his travels. In his case, the cloaking mechanism does still work, though he has no idea why. Because of this it can take many shapes and forms dependent upon where he happens to be. This has come in handy many times, and has allowed him to walk freely among those who are unaware of who he is. At present he tries to stay away from drama, having witnessed many great battles. He's by no means a coward however, and would look down upon anyone who would think to suggest this. It is his view that there is a time and a place for conquests, but right now he is more interested in experiencing a range of activities!