Awhile back, I created a plugin that would allow you to put a template tag on your site to display popular posts based on the number of comments on posts. It was quick, dirty and not the best code I have ever written.
I have completely rebuilt it using the WordPress Widget system so you can add it to your sidebar via the Widgets Administration panel.
This widget works based on the number of comments on your posts. It takes the most commented post and gives it a value of 1. You can then pick up to three levels to compare the other number of comments per post. You can also pick the number of posts to display in your sidebar.