Here is how it goes:
Start by importing a logo.
I used the cow logo. But you can use any logo, still or video.
The .ai-file is 200px*200px
Create a new composition, name it ring. Mine is 1000px *1000px (it's big, so we have a lot of room), 25 frames, 10 seconds long.
Put the logo into the new composition.
Press Cmd+D(or Ctrl+D) 24 times, so you will have 25 Cow layers in total.
Create a Null object.
To make it a lot easier, make your composition window a 2 view. One the active view and one custom view 2.
Make all the layers, including the null, a 3d object by switching the 3d box on.
Select the first layer and then shift select the last one.
Now parent all the layers to the null object.

Change the z-position of the cow layers to 400. But you can choose less or more.
Change there y-axis to 180°.
At the Null, set a x-rotation keyframe at 0 and at frame 25 or one second(PAL)add another of - 345°.

Unparent the last layer from the null layer at the beginning of the timeline.
Cmd(or Ctrl)+right arrow to go one frame further. Then unparent this also from the null object.
Do this for all the layers.
When you look in the custom views you will see the layers get placed in a ring position.
Why do we choose 25 frames? Because there are 25 layers. So whenever we go 1 frame further in time, the position of each layer change because of the parent with the null.
So now we have a ring. But it looks like there overlapping each other.
Select all cow layers and change the scale to 40. Now you will have a space between each layer.

Select all layers again and parent them again to the null layer. You can delete the keyframes of the null layer.
Make another null object and name it controller. Parent then the null 1 to the control null.

Right now you can do whatever you want to do with the ring -- scales, rotation or whatever.
Add a camera to have more perspective. Use a 35 mm or your choice.
What if you don't want the inside to be the cow logo, but a color?
For the color:
- In the beginning of making the ring, make a precomp from the cow layer(Cmd or Ctrl+N)
- Make 3d.
- Duplicate the layer.
- Make a change with 1 in z-postion.
- Add the fill or tint effect. Change it the layer 2 whatever color you want.
- Also rotate the y-axis to 180 for the first layer.
- Add this precomp to a new comp where you want to build to ring.

Then do the process over again. And turn on the collapse transformation(sun) button for those precomped layers.
Making this a precomp in the beginning is best so that you can then change the logos or stills and use it as a template.
That's it! Play around with it, there are unlimited variations to make.
Feel free to ask questions in the After Effects forum at CreativeCOW.net.