I have been searching all over to find a tutorial (for Photoshop or Illustrator) to create something with this look:
I would like to be able to achieve this with different textures (wood, stone, glass, etc.)
The best way to do this now with Photoshop CS6 Extended is with the redesigned 3D tools/features. I would assume that you are starting off with vector art—the sample looks like one of the standard Shapes in the Shape Presets. Make your text, vector art, shape, path, selection and then Convert to 3D Extrusion (not Postcard as you'll want to use the Cap properties).
When you create the 3D layer there are two panels you'll work with 3D and Properties. Select the 3D Shape you created and then in properties change the Extrusion depth to something like 10. Next select Cap from the Properties panel and adjust the Inflation (Puffyness) either with the Property input files, or using the On-Canvas HUD controls (Bevel is on the left and Inflation is on the right) that appear over your object. It all happens in real-time and is non-destructive so you can go back in and change the path (if that's what you started with), text, etc... I'd say an inflation value of 5% would be enough to get you what you want.
Once you have it done you can also play with lighting, Bevel (if you wanted to create a little highlight on the edge of the piece or change the color/material), Deform, etc... There's a lot of power there so have fun!
The last thing you'll want to do is Render the 3D layer. This takes a little time but provides much better results than the real-time GL preview. Also, if you have shadows from lights or transparency from materials in the 3D layer, when you render they become transparent as well, so if you save to web, they will let the background pass-through—a great effect for web buttons and banners.
More information on Photoshop's 3D features can be found at: http://www.photoshop.com/products/photoshop/3d
UPDATE: I had just remembered your post and tried to see what I could do. It took about 2-3 minutes to set it up and 3-4 minutes to render...
It's probably a little too puffy and I should have used the Bevel with a rounded Contour, I didn't remove the shadows caused by the lighting, blah, blah, blah...
With another minute or two I change the color and went from using Inflation to using just the Bevel, rotated the lights, added some transparency to the front and side and set it to render (for about 5 minutes)...
I think this is somewhat what you were asking. If it could be changed to brick...
...or wood (with a reflective floor)...
...and the answer is yes, and Photoshop CS6 Extended makes it easy.
Steps again: Make Vector shape, Convert to 3D, Modify Caps, Apply Material, and Render. Now go ahead and +1 my answers. (^_^) Cheers!
If you want to accomplish this in Adobe Illustrator, take a look at some Gradient Mesh tutorials.
You can easily do this with the Bevel and Emboss option in Photoshop. Just double-click the layer and go to Bevel and Emboss. Play with the parameters a little.