We just got resupplied with a couple of cats, including one inquisitive kitten. Dangling curtain cords were too much of a temptation. So I got some stir sticks (mine are a bit smaller than typical Popsicle sticks) and made some cleats. Stores sell curtain cleats for a couple of bucks and nicer ones can be had from marine supply stores.
Step 1: Snip/saw, Glue, Assemble
You need two sticks per cleat. Snip or saw one stick in half. Shape and sand as desired. All three sticks will then be glued together, with the two short sticks centered in the middle of the longer stick. If you prefer to have smaller flanges at each end, then simply shorten two full size sticks to the length you desire. Add an additional short stick if you have large diameter cords and need a wider gap.
Step 2: Drill, Nail and Paint
Drill a couple of small holes for your brads or nails. Nail the cleats a foot or two below the top of your curtain, with the short sticks closest to the wall (seems obvious until you nail one in backward like I did). Attach them far enough out from the curtain itself so that the curtain won't hang up on the cleat as you raise or lower it. The cleat typically goes on the same side as the cord. :-)
I wasn't sure how well these were going to work so I did a test run for a couple of days before painting them to match the wall paint. You should paint or stain yours first.
While not as nice and polished as Dr. Joe's Otter Sculpted Jam Cleat, they are quick and dirty and essentially free to make.
If you were too late and your cat has already chewed up a cord, check out MajikTime's Instructable called "Repair damaged Pull Cords on Horizontal Blinds".