Three anime series that I think have excellent conclusions are Ouran High School Host Club, Azumanga Daioh and Rumbling Hearts. The Ouran anime series is a manga adaption and because of that, they are often incomplete. The television series adapts part of the manga, but the anime creators did a good job tying several of the loose ends. I did not longe for more Ouran High School Host Club anime because it had enough closure.
In the case of Azumanga Daioh, the conclusion was very good because the path of all the girls was clearly defined. It might be easier to conclude a slice of life anime, but I want to give credit where it is due. Another series with a very good ending is Rumbling Hearts. I realize that this series has some defficiences (like poor animation and over the top drama), but the conclusion is very satsfying because it has closure, even if it is sad.
Next, I will give examples of unsatisfying conclusions and lapses of logic. Neon Genesis Evangelion is a great series that has suffered some criticism because of its ending. The last two episodes should not ruin the legacy of Evangelion in my opinion. As far as I know Hideaki Anno had to patch up an ending for the series because he ran out of funds. I will give Anno the benefit of the doubt because the rest of the series is pretty much flawless.
Another revered series that could have used more closure and logic is Cowboy Bebop. At the end of the series the audience does not exactly know what was going to happen to Spike, Faye and Jet. I criticize Cowboy Bebop because its conclusion is too hectic as we see how thing accelerate very rapidly in the last three episodes. Things that I did not think were there, existed (Faye's love toward Spike for example).
I hope I made my point and showed that conclusions are not the most crucial elements when determining what makes a great anime series but are important. In the cases of Evangelion and Cowboy Bebop, their conclusions might have damaged their overall reputation just a bit. It is also possible for well done conclusions, with closure and logic, to elevate the reputation of series like Rumbling Hearts.
Early next week I hope to end the discussion talking about originality/uniqueness and production values in anime series.