Seeing as I am not really in a position to necessarily need a project management system, I don't know if I am particularly the best candidate for a debate. Nonetheless, I strangely enjoy playing around with them. Lately, I have used clockingit.com. it is more for time management but I really like that I can make notes of my work so that I am constantly tracking what I am doing. It has a built-in forum, chat, file management and a place to set up notes. I haven't particularly used those extra features, but the layout is really nice and you get used to the system fairly quickly. There are also lots of cool features you end up using the more you stay with it. The best part is that it is completely free and you get to customize it a bit as well as having a link to your team's page.
I want to use it with a college magazine that I work for, but I have struggled in the past to get them to adopt tools like these as we're all students and they'd just rather check their email and deal with task/project management in their heads. So instead I use it as a kind of note-taking app and journal that tracks my time and keeps me thinking about what I am doing.
http://www.clockingit.com/
I'd like to see more free options like these. One feature that I would really like to see is better idea-management. I haven't seen anyone that has done it right. I could just have this idea in my head though that I won't let go of. I want to see ideas organized similarly to projects with features and attributes that you can discuss and modify. Essentially I want a system that allows me to think of an idea/project like a program and each attribute and feature can be arranged in hierarchical or folksonomical way and then everyone can discuss their stance, comment, modify or add more. This isn't really the place to discuss this, but I thought I should elaborate on what I want.