These primarily apply to single-player video games.
1. Solid, ORIGINAL gameplay. I don't mind when games take inspiration from another game (See: Terraria being inspired by Minecraft), but outright copying another game drives me nuts.
2. Replay Value.
3. Challenge. I don't want a game that plays itself. I want to feel satisfied after beating it. Just make sure the difficulty is fair and not artificial. Dark Souls 1 and 2 are the shining examples of fair difficulty.
4. Not every game needs a story. However, if you do have one, make it a story worth telling.
5. Strike a balance between freedom and directing the player. Too many "open world games" today have no sense of direction, and just feel empty or pointless as a result. See Fallout 3 for a fantastic example of how to do this correctly.
6. Make the game memorable from start to finish. I played Rage recently. That game started off pretty strong, but had one of the worst endings I've seen in a long time. It almost ruined the entire game for me.
