For those who loved Base Camp but hated the fact that it had no issue tracker, task management, etc., there's a site out there called GoPlan, http://goplan.info/. I really like what I see at first glance here. Base Camp-like simplicity and easy-on-the-eyes design are king here, but it's not completely feature-incomplete, either. And I like the fact that besides its limited free package, its smallest complete package is moderately affordable at $10. I could afford that.
This is really just for lightweight project management. For real PM and issue tracking, people seem to be using Trac a lot. But you have to host it. If you have a dedicated host or are hosting it internally, and in either case if you have virtualization support (i.e. VMWare Server), try getting Trac from Jumpbox.
UPDATE: Sahil Parikh [sahil@deskaway.com] pointed out DeskAway.com .. I agree with him, it's much more complete and has a lot more features for a new user. Doesn't have the appearance polish (I hate the amateurish logo, for instance, and the whole thing just looks white-washed) but that's a fuzzy feely measure. I can see myself using this, for sure.
UPDATE 2: I've been trying to use DeskAway.com, but it has some usability issues. For example, the default phone number for a Contact record is Mobile, not Office, and there is no obvious way to make the Office number the default contact phone number. Worse, enter xxx-xxx-xxxx and it will clear the whole number out and scream at you for entering an invalid number. Enter it without the hyphens and it takes. (?!) And if you add a Company record, you can't add punctuation or symbols at the end; it will not let you. I got past it by inserting inside text rather than appending at the end. But.., I mean .., ?!! And to top it off, it refuses .docx files. And when you report this stuff, it asks you to select your operating system: Vista, XP, Mac, or Linux. Windows Server's not in the list, and it's not free-text. I hate these kinds of issues ... I'd prefer fewer features over dealing with these issues.