Like children commenters said, comments are very useful if there's a community around your site. For my personal blog, comments were mostly "thanks" and sometimes angry comments about how I didn't like the thing they liked, although these were rare.

There were sometimes helpful corrections, but those came largely through email anyway, and, since I update the articles when I receive a correction, the corrective comments instantly became obsolete.

I just remembered the biggest reason why I removed comments: Spam. The added value wasn't significant enough (due to the reasons above) to warrant spending the time I spent removing span comments. Make a popular post and you'll get a whole bunch of "What a great post! Check out my thing: <thing>". I didn't want to spend more time moderating so I just disabled comments.

I think comments provide value everywhere where there is a community. If you don't have a community around your website and only random strangers visit it, it won't offer considerable value. Although I cannot say that I have a community around my blog, I occasionally get useful comments with clarifying questions and additional information which helps me improve my content.

For blog-posts which contains technical how-to information, the comments often contain corrections or other additional information which may be relevant for later releases or other distros.

I’ve certainly found that useful more than once.

Yes, this is one example of useful comments. It's just that, for my site, those tended to be over email, which I generally respond to immediately, so it's equivalently useful.

Comment sections are especially good for sites which the author doesn't update, so you can read the correction in the comment.

Many blogs I frequent have highly interesting comments. For example on LanguageLog the comments are often more interesting than the articles.

At any blog that is not just made for marketing.

Shared blogs (those with multiple authors) and podcasts often have lively discussions in the comments. For example, http://www.econtalk.org/amy-tuteur-on-birth-natural-parentin...