First person shooter
Perhaps the easiest to envisage, you want down a real street, but see virtual enemies that you can shoot with a virtual weapon (although you might actually hold a controller or dummy weapon in your hand). You might be able to shoot real people too (even if they're not playing the game).
Real time strategy
You are in the thick of a war. You see all the units you command around you, and the enemies in the distance. You order where your units go, and what they should attack. Ideally the computer would recognise verbal instructions, but the game might be augmented by head-up display that shows you a map of the area and where you units are deployed, allowing you to move them about as needs be.
As the physical presence of the person in not necessarily part of the game, it would be possible to have the game on different scales, for example a game with toy-soldier sized units on the living room floor.
The real-world economy becomes your virtual playground. You can virtually own businesses that exist in real life.
As with the first person shooter, but with more depth. Wielding a sword (even if plastic) whilst walking down the street may get some unwarranted interest, however. And there is the issue that you cannot "level-up" your physical self as easily (although the power of your weapons and spells would be in the virtual world and therefore able to increase in power).
Turn any surface into a platform game using edge detection. The player control an avatar running, jumping and fighting along that surface.