For games with a story, I would like for a sequel to continue the story in some way. Overall, I'd like for a sequel to:
- Improve on the mechanics of the first
- Work well as a standalone game (it can have a recap of the story, but the player shouldn't have to play previous games to get caught up unless they want to)
- This doesn't apply as much these days, but I'd like for it to have improved graphics as well.