Login requirements exist for one very simple reason: making sure the reporter can be contacted for the inevitable follow-up questions. "What OS are you using? What version of [product]?" etc. It's a barrier to hit-and-run bug reporting where a brief, useless report is placed with bogus or absent contact details that prevent follow-up. Sure, you could just close them, but there *is* a balance needed between time of project contributors and time of bug reporters.
So: I do approve of bug trackers requiring logins. That said, I'd really like to see bug trackers like Bugzilla and JIRA adopt OpenID support, so I could use any existing login to gain basic submitter rights in exchange for giving the tracker a verified email address.
Personally, the only thing that annoys me about most trackers is that I have to create a login just for them with their particular password requirements, etc, and keep it up to date. It's a pain. I don't mind having to log in, I mind having to create and manage the credentials for yet another site. I report a lot of bugs across a wide variety of packages and libraries (in the Linux and Java worlds) and keeping track of the trackers does drive me a bit nuts.
Having expressed my support for login-required trackers, I do think it worth noting that PostgreSQL's "tracker" (the pgsql-bugs mailing list and the report form on the website) doesn't require login. There are a *lot* of reports that're really just "how do I do X" questions, questions about other products, etc, and I suspect they're posted there mostly because it's easier than the main mailing lists. Rather than making filing bugs harder, perhaps making asking questions easier is the trick, though, given that these days people are unused to and scared of mailing lists and seem to prefer web forums (blech).
Anyway, bring on OpenID for bug trackers! Oh, and a central bug tracker directory to find the tracker for a given project, while we're wishing.