IMHO, the biggest use case for 3D right now is to add affordances to current flat interfaces. Many interfaces already incorporate 3D affordances, usually demonstrating depth to help the user understand what is happening, but these affordances are almost always faked, the same way that 3D is often faked by photoshop wizards.

At famo.us, we hope to make it much easier for interface designers use real 3D effects to add affordances to their interface and explore how else 3D can be used. Previously, if you wanted to design a 3D interface you had to completely invest in 3D, which is expensive time-wise to do for the sake of experimentation. What we'd like to do at famo.us is bridge 2D and 3D in a way that you can build your interfaces using familiar 2D paradigms, but also give you the tooling to explore 3D using real content you already have in 2D.

As more designers explore 3D and more customers become familiar with 3D little by little, I think we'll see more and more examples of its utility.

Here's a video where 3D is used with a constrained z-depth and orthogonal camera position (i.e. elevation view).

http://famo.us/ (the video on the left)

Also take a look at Clear App to see small examples of how 3D has been used to add affordances to a mostly 2D interface.

http://www.realmacsoftware.com/clear/