Star Trek: TOS: As I mentioned, this series was cancelled by its third season. But it participates in my phenomenon because it was only a few years after that they came out with the first movie. The movies were way better than the series ever got.
Star Trek: TNG: I happen to think every season of this series was wicked but to show the phenomenon's occurrance in this series I present the fact that the Borg made its best and most famous appearance in the season finale (The Best of Both Worlds)of season 3. The Borg made their first appearance in Q Who? in season 2, which was good, I think the season 3 finale proves my case. The Borg didn't appear that much after this episode but when they did it was wicked. Q is another of my favourite reaccuring characters, and he appeared in the very first episode. But the average episode in the succeeding seasons was better than the average episode of the first 3.
Star Trek: DS9: I didn't watch this show at all when it first came out. I only took interest in it later when I saw an episode from the 4th or 5th season late at night. I watched every episode the summer I had to work nights at the local coffee factory. The first appearance of the Dominion was in the season finale of the 2nd season, but that episode wasn't very interesting. The season 3 premiere was cool, as we learn who the Dominion are and the origins of Odo. The start of the Dominion War and everything else happened in this season. It was the most innovative thing I have seen to date on a Star Trek series. It defined this series. This series is the best example of what I am discussing here.
Star Trek: Voyager: First off, let me just say that Voyager sucked. By the end of season 2 it lost 31% of its viewers. The season 3 finale brought it back to life, barely. Scorpion was the first appearance of the Borg in this series and went on to "define" the series. They used the Borg too much and destroyed it's credibility as a cool villain. Oh well, it got "better" in the 3rd season, that's all I am going to say here.
Star Trek: Enterprise: I waited this long to write this article to see how the 3rd season turned out. It too displayed the phenomenon. The season 3 premiere began the ship's journey into the Delphic Expanse, well the season 2 finale did but the season 3 premiere began the actual storyline. The difference here is that in DS9 and Voyager the season 3 story arcs set the stage for the rest of the series, whereas in this season they ended the Xindi story arcs in the same season. I think they may bring the Xindi back but for another storyline altogether. The season 3 finale was wicked as well.
If they make another series after Enterprise then I will update this.