You could check the lists on dramawiki. I know the
kdrama list is updated, and I think the
jdrama list is complete as well. You can see the end date on the Korean list so you can find ended ones easily. For the jdramas you'd have to click through. There's probably a better way for the jdramas, but this is all I can think of at the moment. Don't know what to suggest for other countries, either.
Edit: this is assuming you meant how to find which ones have recently ended. Not how to watch a series that has recently ended :)
