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