The simplified purpose of Stack Overflow: be a better Q&A site; raise the bar for finding answers above "trawling through a forum."
SO achieves its goal by making questions editable (and well-moderated) so they don't suck; making answers editable, like wikis, so the best answers get better and more complete over time; and allowing voting on posts.
Here's how comments are breaking the system:
- Comments on a question are higher on the page (more visible) than the greatest possible answer
- Comments don't head to oblivion with downvotes, or even get surpassed by other comments. (Example — the first part of the comment thread is shown to be incorrect by the first answer).
- To get the best information about a problem, it is now necessary to read not only the question and all the answers, but also a mini conversation about every single one.
- It's quicker and easier for people to comment on a question or answer than to actually edit the post, but less useful for actually understanding/solving problems.
- Comments regularly answer questions — or provide different solutions within an answer. (Example)
I can understand comments as a meta part of SO; i.e. as behind-the-scenes discussions that lead to improved questions and answers. But the current, highly visible implementation is causing a drop in Stack Overflow's ability to server its purpose (as I understand it).
P.S. This will probably be an even bigger problem amongst communities that aren't as technical and well-moderated as SO.
I'm sure this has been discussed in depth somewhere but the most detailed answer I've seen so far — largely about functionality of comments — pretty much says they are useful for things that are either meta discussions or should be merged into a question or an answer.