I'd go with Atlassian's Jira, which is free for open source & academic
projects and can act as PM tool as well, can be integrated with
SVN/git, and a bunch of other tools to fully support the whole
development process, including tests&QA and so on.
Of the other mentioned, I'd dealt with Trac (seems much
devels-oriented), Mantis (non that friendly and somehow contrived for
some aspects, but I didn't use it so much) and RT (which is just a
ticketing system IIRC).
I'd go with Atlassian's Jira, which is free for open source & academic
projects and can act as PM tool as well, can be integrated with
SVN/git, and a bunch of other tools to fully support the whole
development process, including tests&QA and so on.
I am looking for a Free Software solution not for a solution for free.
Therefore Jira does not qualify.
Of the other mentioned, I'd dealt with Trac (seems much
devels-oriented), Mantis (non that friendly and somehow contrived for
some aspects, but I didn't use it so much) and RT (which is just a
ticketing system IIRC).
As everyone already said, it depends a lot on your use(r) case.
But for general lus..ehm..user access, I used sometimes osticket: http://osticket.com/
The old 1.7.x series was pretty limited, not multilingual (but
customizable) nor multiproject but very simple for just opening/tracking
"support tickets" for a small user-base of both users and technicians.
Unfortunately now seems discontinued (or i just missed it on the
download page).
I also tried some times ago both the 1.8.x and the 1.9.x version and
they was just too bloat (for my use case) (and pretty insecure, at least
reading the last security bullettins seen on various mailing lists <g>),
but maybe they're worth a try.
For a "developer shop" I whould just go with trac/gitlab/redmine.