What I decided to do is to refer to the name of the city/town as it was known when my ancestor lived there. For example, my grandfather was born in Nagyszeben in what was then Hungary, which today is the city of Sibiu in Romania. It didn't seem appropriate to refer to it by its Romanian name as this would have implied that he was of Romanian descent (he certainly would not have called it by its Romanian name!).
The name of the country each place was located in was also a problem. Once again, it would have been historically inaccurate to record one of my ancestors as having been born in Slovakia when that country didn't even exist at the time. I ended up setting up a separate entity which I called "Greater Hungary" to cater for these situations but also record their present names in the comments.
I concede that this is not a solution for everyone and would also like to know how others deal with this problem.