How about the Puzzle genre?
- Challenging Puzzles
- Some sort of plot (in depth or just there because it needs a plot)
- Either shallow characters that are just there or characters that have detailed backgrounds that are explored throughout the game or subsequent games
- Possibly no characters and no plot depending on the game
Actually, I think that might be just about everything. There's not a whole lot to the puzzle genre, and this list was made with games like Professor Layton in mind.