Disqus is likely the most widely used commenting system on the web today. It has many advantages. The one I find most convenient is that all of your Disqus comments are linked into one account and you don't have to enter credentials on 50 different sites when you want to comment. I even use it for the comments here.
If you have an older Wordpress blog you probably have thousands of comments with the built in comment system. The steps to migrating over to Disqus are as follows: