I believe that Final Fantasy XI can be completed. If you play far enough, there are clear, concise endings written: the current storyline you are playing ends completely, there are cutscenes playing for several minutes, there are credits rolling at the end of it. For example, the original Final Fantasy XI ends when your party defeats the Shadow Lord — the game goes on — but the storyline does not until you buy the sequel expansion pack.
I have completed all of the numbered Final Fantasy games except for Final Fantasy II and Final Fantasy III.