Something that has a gripping storyline. If something isn't immersive and doesn't draw you into the story, then it can't be deemed as a good game, imo. There are exceptions where you have games like Wario Ware, that are just mini games, but that is a different type and isn't classed in my description here.
Basically, the main elements that need to be 10/10 for me are storyline, music + sound effects, gameplay. As I stated above, without an amazing storyline, you risk not having the audience engaged in the game and run the risk of them putting the controller down. With the music and sound effects, you need something that can help with the immersion of the story. The music is there to add feeling too, so having good, well planned out music and effects really goes a long way; it is also nice to not be annoyed by the music when playing the game.
Finally, gameplay. If the game mechanics are just annoying or clunky, then you are going to get frustrated with the game and not enjoy it.
Just what I look for...