A Link Between Worlds is a masterpiece and required for any Zelda fan. Pokemon X/Y is also great, as is Fire Emblem and Bravely Default. Basically, what's on Skyblade's list.

I could go on with others that everyone else has mentioned but here are two that I doubt anyone will mention since they are fairly obscure:

9 Hours, 9 Persons, 9 Doors (DS)
Zero Escape: Virtue's Last Reward (3DS)

VLR is the sequel to 999 and they are both adventure point-and-click style games but the storytelling is phenomenal and both games branch into multiple endings (which you can then rewind to see the other endings).