Typically the entire game world will be in 3D. This does include explosions and debris, however typically explosions, grass, and other particles are drawn as 2D "billboards" which can look kinda bad in 3D if it's on the screen long enough to notice it. Most games will set it up such that the world goes "into the screen" rather than "popping out", since this is usually less jarring for the user. The UI (life bars, radar, ammo counters, etc.) will usually be drawn so that it's "floating" on top of the game world which can look really cool.
The quality of the 3D definitely varies from game to game. One important aspect is making sure the parallax isn't too steep based on what's currently on screen and how far it is from the camera...if it's too steep, some things will "tear apart" (basically the images are too far apart in the right and left eye and your brain can't put the images together) which is a really uncomfortable experience. Newer games definitely do a much better job with this than some of the older ones.
If you do decide to go for a 3D TV, I would recommend going for a passive TV. The one we have at work causes much less headaches than the active TV's, and you don't have to buy ultra-expensive shutter glasses.
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