Generally there are two types of sidebar on a website: the one with contents relating to the main content on the current page, and the one with contents relating to the entire website.
The classic WordPress widgets examples are the building blocks of the latter type of sidebar: “Recent Posts”, “Categories”, “Archives”, “Meta”. Meanwhile, examples of the relatively rare example of the former type are related videos (as in YouTube), quote highlights in interview articles, footnotes placed to the side of its corresponding sentence, or even comments (as can be seen in Medium’s brilliant context-specific commenting system).
I appreciate the former type much, much more than the latter. Website-related sidebars, especially when poorly designed, often distract instead of support the main content. This is especially true on single article pages, which oftentimes is the most frequently visited area in a website, not the homepage.
On the other hand, the former type of sidebar adds to the content instead of substract attention from it. It adds immersion. It can gently leads to other parts of the website, whereas website-related sidebars can feel forced at times (“Like my coding article? Take a look at my Personal posts category? No? How about the archive from December 2002?”).
Understandably, it requires more effort to develop a system where sidebar contents can always support the main content. It’s not always easy to gather supporting contents. In that case, instead of a fixed sidebar area, a flexible asides system can be employed. An example can be seen in The Great Discontent.
As for website-related sidebar contents? I feel that the footer area can be best employed for those. It doesn’t get in the way of the main article, but it’s always there whenever somone needs it.