what project management tools / softwares do you use and how does it supports managing the requirements, some kind of traceability to the implementation, bugs, etc. ?
I use Basecamp (http://www.basecamphq.com/). It's not specifically geared to software projects, but then most of the really thorny problems in any real-word software project are the peopleware issues, anyway.
Basecamp is really lightweight and doesn't constraint you into using specific models.
As it's not developer centric, the non-techs are happy using it too - which is pretty essential. It does have default message categories of "Bug Report", "Feature Request", etc, though. However, for managing bug cases I use OnTime - as it's more directly focused on that task.
Beyond that we use Skype (IM), Twitter and email.
I really love Pivotal Tracker it is great for managing development tasks. First of all it is free. Second it is advanced enough but still user friendly enough to help me out during development. Actually we have started using it at work for managing tasks.
Even though its really a bug tracking system we use Jira to store and manage requirements etc. It also includes reporting etc. As long as all of the developers enter accurate information it can help aid some management decisions.
We use VisionProject and chose this for the reason that it works so good for developing software from the requirement phase to the end, including the support phase. It also includes a public support module for the customers to follow their issues.