I would recommend 'Chrono Trigger'. It has a time - traveling story that is really well - written. You get to see different eras and how your actions in one time period can affect others. 'Dragon Age: Origins' is also good. The story varies depending on your chosen origin, which gives a lot of replayability. There are deep political and religious themes, and you have to unite different races to fight a great evil. Then there's 'Mass Effect' series. The overarching story about saving the galaxy from the Reapers is exciting, and the character development and choices you make throughout the games really matter.
Some RPG games with great stories are 'Skyrim'. It has a vast open - world story that lets you be a part of different quests and factions. You can be a hero or a villain depending on your choices. 'Divinity: Original Sin 2' has a very in - depth story. You create your own character with a unique background, and the game has a lot of reactivity to your choices. There are also multiple endings based on your actions. 'Baldur's Gate II' is a classic. It has a deep and immersive story filled with memorable characters and challenging quests.