I have said a lot about Basecamp over the past few years. I have been a user for a while now, and the service now is better than ever. Sadly, most of my clients were not using it, so the $50 I was spending per month to organize my projects was not seeing a return on investment beyond personal use (and that does not count in the bottom line).
There is a free, open source, project management tool out there called dotProject. Since it is open source it is quite rought around the edges. It can do so much more than Basecamp, but it is at least 10x more complicated, even to do simple stuff.
It can handle time tracking down to the minute detail, and can even do invoicing if you use an older version (that of course I am not using). One thing I miss is the To-Do lists from Basecamp. A third party has developed a To-Do like module called "Action Items" but it, like most of dotProject itself, has a clunky interface.
But in the end it is the bottom line that matters, and saving $50 a month is worth the idiocyncrisies of dotProject. It is a good piece of software and keeps me on task, so in that reguard, it does exactly what I need it to do.
Now I just have to figure out how to create users with limited access! I know it is possible as the software has pretty granular permissions. Thankfully there is an active community forum to answer questions.