Where am I supposed to report a broken DOI? Where am I supposed to report a broken DOI? To https://www.doi.org/, to the  DOI registration agency that issued the DOI, to whoever is responsible for the website to which the DOI points to, or to somebody else?

For example, http://dx.doi.org/10.1016/0364-0213(90)90002-E is 404:
It's not likely that the DOI itself is broken. However, a number of things might be happening to prevent you access to the material (I'll assume it's an article) or, more commonly, human error is at play. First, make sure that there's been no change to your the proxy settings, firewall or security settings on your computer. Sometimes, these settings return a "DOI not working" error.

If you're sure that there's nothing wrong with your system (say because you're accessing a DOI for an article from the same issue of the journal), then I suggest that you inform the journal about your error. The web staff of a journal are able to respond to these reports rather quickly. They'll also be able to determine whether the result is due to a coding error or an editing error. In one case just recently, we caught an error in the DOI from being published on the manuscript. The error was due to an intern who was unfamiliar with copyediting notations on the galleys. (As I said, human error.)

I don't suggest that you report to doi.org. They'll collect information, but pass it on to the journal and may miss something material. Contacting the journal is more efficient. Finally, contacting the journal will also allow them to send you a copy of the article you wanted to access, while you wait for them to correct the issue.

PS. I remember a while back when there was a DOI "blackout". None of the DOIs for our articles would work. We were swamped with requests. Our webteam went nuts looking for the error. It turns out that this was a human error issue, but at the DNS level. I'm not a computer expert but the head of our web team explained it to us like this: "Someone forgot to renew the license for the dx.doi.org account."

Good luck!