@frazzle and everyone else:

Take a look at this animation short. It's an FLV file, so you'll need a Flash player to view it (I use this free player):

http://www.mediafire.com/?9wxxn2xh4om

Certain parts of this feature showcase the 2D yet still 3D effect I'm talking about. Here's the original Disney short that inspired the creator of A Vampyre Story:

http://www.youtube.com/watch?v=UMwa3ZwTwyA

It also uses the layered 3Dish effect and was Disney's first foray into that technology. They used it a lot in Snow White and throughout many of their features and shorts ever since. It's nothing revolutionary in the world of animation (anime features Akira and Ghost in the Shel, as well as Batman The Animated Series used it a lot), but you don't see it a lot in 2D or 2.5D games. It's usually more along the lines of your standard parallax scrolling effect seen in side scrollers. A good example of that would be the Limbo trailer. That forest stuff at the beginning feature your run of the mill parallax scrolling; however it's still very similar to what I'm wanting to do:

http://www.limbogame.org