Polar Grid Tool Method
:: Quick and dirty ::
- On the Tools Palette, click and hold on the "Line Tool".
- Choose "Polar Grid Tool" from the drop-down
- Begin dragging your shape, but don't release the mouse button
- Pressing the arrow keys in this "unreleased shape" state will alter the number of line dividers, and will yield something like the result you seem to be asking for.
If that won't suffice, you either want the Scaling Tool or Blending.
Scaling Tool Method
:: An overlooked fundamental ::
Select you shape with the Selection Tool, then choose the Scale Tool (keyboard shortcut: 's').
In this instance, you'll want to press "Enter" with the shape selected to bring up the Scale Tool Dialog, tweak the settings, and choose "Copy" at the bottom of the dialog.
Press Cmd / Ctrl + D to repeat the effect the desired number of times.
One setting to pay attention to in the dialog is "Scale Strokes and Effects".
As you can see, the strokes in this example are not increased as in the other result:
:: Powerful but sometimes more than necessary ::
- Make one circle sized as your innermost circle, and one as your outermost.
- Select both objects.
- In File Menu / Menu Bar: Object > Blend > Make
- This probably won't yield the desired results, so again from your Menu options, choose Object > Blend > Blending Options*
- In the dialog, for "Spacing", choose either "Specified Steps" or "Specified Distance". Tweak the numbers until you a result you like (make sure you have the "Preview" box ticked!)
*Alternatively, you can double-click on your "Blend Tool" in the Tools Palette to bring up your Blend Options dialog box.