In my previous post I discussed the basics of what a Coding Dojo is and why you'd want to have one.
I host a Coding Dojo at my work every month, so I've decided to periodically update an index page of example Katas. They are usually based off existing Katas which are available on the main Coding Dojo website. I'd also recommend the prolific Sao Paulo Coding Dojo.
You should be able to reuse the same problems at your own Dojo. If you have any other recommendations then please email/twitter me, or comment on this post.
On a slightly related note, I just completed the common Minesweeper Kata.
Matt Wynne, who has an excellent blog, recently created a test harness using the Ruby BDD framework called Cucumber. It acts as a great way to introduce you to BDD and Github if you haven't used them before.