In this example from Portal 2, most of the scene is deep in the screen, but as you get close, the corner of the wall's panel door is peeping in front of the screen.
In the above case, the scene is deep, but the corners of the box are clearly in front of the screen.While it's best to be able to get the character to pop out just in front of the display, this can be difficult because of camera angle issues when the scene changes.
In Batman Arkham Asylum, Batman's figure is just in front of the display glass, while the rest is deep in the screen.
