I've been wanting to use bottle caps as checkers, but I wanted to add something to them to give them more of a checker 'feel'. Adding clay and a base to smooth things out seems to work well.
Step 1: What You Need
Bottle caps (24 - 12 of two different designs or colors).
Clay (I made my own using a simple recipe I found here: http://chemistry.about.com/od/chemistryactivities/a/modeling_clay_recipes.htm (I used the first one)).
A butter knife to cut the clay
Something for the base (I used vinyl because I had some laying around. Felt or some other fabric would probably work well, if not better. Or I suspect a nice coating of glue would do the trick).
Scissors (To cut out your base fabric, and to trim it when it's dry).
Step 2: Using the Clay
Roll the clay into a 'log' relative to the size of your caps, then cut slices to fit inside. You'll want the clay to be fairly flush with the bottom of the caps.
Squish the clay in to make sure you don't leave any gaps. Use extra bits of clay if your cut was too small, or remove excess if it was too much , and smooth everything out.
Step 3: Allow to Dry
Once you get the clay fitted into all your checkers, allow it to dry before you add the bases.
Step 4: Adding Bases
Place a cap on your base material, trace around it with a marker or pen once for each checker you're making, then cut them out.
Put a nice layer of glue on the bottom of each checker, and add the bases. Allow them to dry well.
Step 5: Complete
Go play checkers!