I'd really like to hear from hackers organizing their projects what software in this category they like best. I have liked Basecamp as a framework for sharing do-list items with colleagues (most of my colleagues and I work independently of face-to-face meetings most of the time) but I am willing to learn about other products or service. Efficency is key. What do you recommend to do best what Basecamp does?
As a designer, I was frustrated using Basecamp before and that made me start Teambox. I chose the open-source way (like Redmine) and a simple feature set (like Basecamp), trying to make a more up-to-date version of what I thought project collaboration should be.
Things I found missing on BC and I did implement on Teambox: a single account (37s got this right later), a real activity stream (Facebook style, reply to anything from the feed), an open-source codebase so others could extend it and tight integration of first level elements: Conversations, Tasks, Pages.
Redmine is great after Basecamp. Minimal, fast wiki. Repository viewers (svn, hg, git). Access control, which can be used to create public pages quite easily. Nested projects.
GitHub's nice if you're focused on building software. Project wikis, home pages, code review, huge open source community.
I just set up redmine about 2 months ago, and I'm loving it. Recently got my SVN linked up and now I can cross reference commits with issues in the tracker.
I absolutly love redmine. Easy to customize, hundreds of add-ons, tons of functionality (including turning off tabs you're not using) and lots of support. If you're a geek that manages your own server, it's the way to go for sure. There's even a "basecamp" theme that looks and works great ;)
I like Open Atrium (http://openatrium.com/) because of its modularity and beautiful deafult theme. It's based on Drupal, so if you were building Drupal websites before then you will find it very easy to customize.
I have yet to find a project management app I like more than AgileZen. It allows me to model my workflow, assess against estimates and to top it off it's very pretty. There are a few things about it that bug me: notifications suck and there is no interaction between projects. Other than that, it's awesome.
Redmine? It has a ton of features, so it limits a lot of the more complicated stuff by default. Notifications are awesome, and cross-project stuff works beautifully when using subprojects (shared gantt, cross linked wikis, timelines, etc).