If starship registries are roughly chronological, and that is a big if, then it is possible that there could be 200 hundred year old ships in operation. I am thinking of the Heart of Gold, which had a registry of NCC-42. I think a ship that old would have gone through so many refits that it might not even be the same ship in the 2160s.
Heart of Gold ? Which episode ?
It's from Conspiracy
, and it's another one of the in-jokes seen only on LCARS (in this case to The Hitchhiker's Guide to the Galaxy
Registration chronology hypothesizing notwithstanding, there doesn't seem to be any way the Heart of Gold
could possibly have had another registry number than forty-two, and the side-effects of the Infinite Improbability drive would very likely have rendered the need for refits pretty much irrelevant.