I personally currently use
Redmine. Parts of it are a pain (the fact that it's a Rails app not being the least of them...Ruby people are seriously messed in the head) but the end result is a pretty complete and straight forward issue tracker with some nice interface touches.
Professionally I use
Jira. Can't really recommend it, but if you're looking to build familiarity with a tool used at multiple studios in the game industry, there ya go. (It's theoretically free for open source projects, but I've never tested those waters)
Both should have 'guest' accounts with modifiable permissions, etc, so that might handle your user registration gripe. (It does nothing to stop report spamming tho) Redmine offers OpenID logins - and most everyone has a Google account - so that might be a middle ground as well...