Star Trek: Deep Space Nine
I would agree with the above. DS9 was the first to really have ongoing story lines, but it didn't start happening until the later series' when the Dominon War started. In Series 6 and 7, the majority the episodes carried on from the previous one. If you watched late Series 6 first, instead of early Series 6 you would get confused.
Also, Voyager was similar with some story lines being continued, but no where as much as DS9. You could watch most VOY episodes without feeling you had missed something.