How important is it to cite the URL in bibliographies?
Including URLs and DOIs can be very helpful. For many if not most articles, a search for the title in a search engine is adequate to locate the paper. Though searching for the title takes longer than clicking on the URL or DOI in the paper, so it's still not preferred in that case.

Further, I've been surprised by articles which are not easily available in Google Scholar but are online. I've made quite a few interlibrary loan requests, later finding out that the entire proceedings of the conference I wanted an article from was online via the professional society which organized the conference. Google Scholar does not capture everything online at the moment. Many researchers do not know how to use the services of their library, so having the URL of the conference paper can be very helpful for many researchers.

Unfortunately many journals and conferences have their own citation style which may not use URLs or DOIs, but when you have the option, I think you should use it. My policy is to include as much helpful information as I can, and that often means more obscure citation information like OCLC numbers and ISSNs (which librarians can use to locate print only items).