First of all, here is the final effect:
YouTube - After Effects 3d Poker Chip Vegas Intro
The video looks 3D (I hope) but uses no actual 3D objects. That means, no expensive software or plugins needed to create a pretty cool effect with tons of potential. I'm sharing this in the hopes that you'll get some good use from it, while also hopeful that someone will help me to improve it.
Basics: I recently learned of a cheap way to make 3D effects using only the Shatter effect in Adobe After Effects. If you're an AE user, I highly recommend googling for tips and tutorials (I learned from youtube), but here's the basic idea: the shatter effect in AE breaks an object apart and the pieces fall in 3D based on different variables. Prior to the actual Shatter, AE renders a 3D version of the object, so if the shatter never takes place you're left with a depth on the z-axis that creates a 3D object. It's very useful for making 3D text, but also useful for shallow 3D objects like the poker chips in my example.
How to: The easiest way to learn is to start with text. In AE, make a new text layer with whatever letters or words you want to use. Then, create a new solid. (I used single color solids, but gradients and even 2d photos work as well.) Here's the weird part - hide the text, and apply the shatter effect to the solid 2d layer. Change the shatter map to "Custom" in the effects properties (instead of "Bricks", "Glass", etc), and then select the custom map in the next selection box - use your text layer as the shatter map. This will make a 3d object using your text as its shape, and using your solid layer or 2d photo as its texture. There are several ways to stop the shatter from taking place after the first frame - I just set the Force>Radius to zero. Then, play with the camera settings IN the effect to see that you've created a 3D object. This is a great way to make 3D logos easily.
Drawbacks and Limitations: Shatter is one of the effects that will allow the use of the Composition Camera OR the Effect Camera. Using the effect camera, as described above, can yield great results if you're using only one object, such as a logo. You can spin around and keep the illusion of 3D with great effect. Unfortunately, when using the Composition Camera, the 3D effect fails. (Imagine that you've drawn a 3d Box on a sheet of paper - if you moved the camera around the piece of paper, the illusion of 3d fails when the camera takes a hard angle to the 2d paper.) To create the above video, I've make every object a child of my main logo - this way the movement of the main logo adjusts the other objects by the same amount, reinforcing the 3D effect. I'd love to be able to rotate, but this is not possible with multiple objects as it ruins the 3D effect. I've tried everything, and can't get around these few limitations.
I hope you find some use for this - please reply with questions, comments and (hopefully) work - arounds to make this more useful.