An action movie type shooter, like red steel in terms of environment, modern weapons but not a War or Tactical game like CoD or Rainbow Six. Maybe like Max Payne even. The pointer shooting would be so clutch in this type of game if done correctly. Then of course a decent campaign and good multiplayer and online as well.
A fighting game but instead of fists and feet Swords, Knives, Axes, Hammers, and Shields. It would need a very responsive system, no pre-programmed slashes. Wii Boxing came surprisingly close to this system considering it was such a small, cheap game, I'm sure if a developer takes time to make a Weapon Fighting game it could work. All the regular options, like Arcade, Training, etc., and online of course.
A sniper game, where its super realistic and you have to deal with Gravity, Windage, etc. No simulated breathing effects, but rather when you go to a high zoom level, the game ups the sensitivity of the pointer so it picks up your actual breathing movement in real life. Imagine having to hold your breathe and stabilize your remote against the floor or other hand when taking a super long shot. That would be awesome. Maybe they could make it into a Hitman-like game, but less sneaking and gunfights, more sniping placing carbombs/poison etc.
As far as ratings they'd all be Teen or Mature depending on the blood/gore obviously.