No matter what bug tracker a project uses, some developers always like to complain about it. This seems to be more true of bug trackers than of any other standard development tool. I think it's because bug trackers are so visual and so interactive that it's easy to imagine the improvements one would make (if one only had the time), and to describe those improvements out loud. Take the inevitable complaints with a grain of salt—many of the trackers below are pretty good.
Throughout these listings, the word "issue" is used to refer to the items the trackers track. But remember that each system may have its own terminology, in which the corresponding term might be "artifact" or "bug" or something else.
Bugzilla is very popular, actively maintained, and seems to make its users pretty happy. I've been using a modified variant of it in my work for four years now, and like it. It's not highly customizeable, but in a odd way that may be one of its features: Bugzilla installations tend to look pretty much the same wherever they are found, which means many developers are already accustomed to its interface and will feel they are in familiar territory.