This is my first take on the new Related Articles Widget.
Please cut and paste the code below to a new HTML Widget from your Page Elements to see if it is working.
I cut and paste the same code to create a new widget, located at the end of this post.
You don't have to get rid of the existing Related Articles widget on your blog. This new one is a totally independent, self-contained widget!
As you can see, the widget forms a query of all the "keyword" (in this case "labels") in this post, queries, and gets a resulting list for the most relevant posts from your blog. It's just like you query a list of terms and get results from the google search at http://www.google.com/ .
The result is, in my humble opinion, a truly "most related articles" relevant set of links, unlike my previous attempts - where only the newest posts from each label showed up. This time, we employ Google's famous ranking algorithm to do the "related" part for us.
I will explain the motivations, excecution and nuances of this "beta" widget in a follow-up post. There are ways to modify the look of the results, such as showing the snippet text or not, or use CSS to alter the look of the widget.
Update: See my explanations here:
Part 1: http://hoctro.blogspot.com/2010/08/dissecting-new-related-articles-part-1.html
Part 2: in progress.