Lately, I was looking for a nice online project management system. The one I found long time ago and I was using is the TaskFreak 0.6.x, which unfortunately is stopped developed right now, although that a new, totally different version is on the way.
I had also the opportunity to use the Basecamp while I was working a few projects with other companies, which is very nice, easy and fast to use. I am sure that I want something like that, but the amount of money is not affordable right now for me.
So I was looking for a free, open source PMS, similar with Basecamp, which I managed to find. It is called ProjectPier (http://www.projectpier.org/) which is what I was looking for. Easy to install, with many features, like Tasklists with Tasks, multiple companies involved in a project, Email notifications, Milestones, tickets and many more.
I downloaded the 0.8.6 version which is pretty much stable, where the 0.8.7 version is almost ready to be released. At their website there is also a video about the v.0.8.8 they develop, with many new features and interface enhancements, which looks really great.
Try this great PMS which looks very good and promising. I'm sure you are going to love it.