Most Compelling Story

I'll go first and throw out Final Fantasy IV. I loved that game from the very beginning to the very end. When things started to seem like a grind through a dungeon, a cut-scene would occur that'd shift to another part of the world, such as Kain and Golbez talking in the Tower of Zot. You'd exit a cave and walk a few steps but to witness the destruction of a castle. It had lovable and hate-able characters. Even though Zemus/Zeromus wasn't mentioned really at all unlike future Final Fantasy antagonists, this game shined through the sheer amount of cut-scenes. Squaresoft really pulled off the six stages of a compelling story which are:

Compelling Introduction: You learn about Cecil, Kain and Rosa and are sent on an obscure mission. Cecil starts to learn more about himself and wants to eventually stop the king.

Past Events and Rising Action: Later in the games story, Tellah is mentioned, as is the other minor characters who die such as Tellah's daughter. This is a pivotal plot device for Edward the Bard.

Climax: The entire story is about stopping Kain and Golbez from obtaining the eight Crystals of the planet. As I mentioned above, the "In other news" type of cut-scenes really helped with climax building. Other than cut-scenes, you are almost always a step behind Kain and Golbez and that builds climax when you're about to catch them.

New Events: Close to 1/3rd through the game, when all seems lost, you hear about the other four crystals of the planet which reside in the underworld.

Falling Action: If there are climax stages in the plots development, there will be falling actions. After Edwards castle is bombarded by the Red Wings fleet, the falling action occurs when the destruction and death count sinks in for everyone. Many events happen through the story like this.

Unexpected ending: There are a lot of unexpected features in this game, such as Kain and Golbez finally turning good and repenting, Zemus being the main antagonist and more.