Take a look at Google Apps ... there are various free project management collaboration tools [such as ManyMoon, Zoho, et al] in the Google App Marketplace that integrate directly with Gmail, Google documents, Google calendar.
The Google Apps business is strictly a mass-market sort of thing, so the stuff you'll find there tends to offer be of the lowest-common-denominator ultra-simple variety. Many of the companies offer a more complexicated premium version of their free tools.
Beware the old axiom ... there is never any such thing as a FREE lunch! You need to exercise some caution before investing too much in other free tools ... somebody else is paying, but probably only temporarily ... if the developer lacks a decent way to monetize the product, the company works for a few months or maybe a year or two and then shuts down. As with other Google products, the Google Apps stuff is largely paid for and supported by Google's ad recommendation engine ... the apps in the Google marketplace might still fail, but at least they have some money coming in and should last a teensy bit longer. What is more is that those advertisements that will be amazingly, remarkably relevant to the issues you are working on in your projects ... you may just get a few ads from competitors or maybe insights into solutions that others offer.
We use PoP Project (www.mypopproject.com). It's a simple, to-the-point tool which is free for now. You can list project tasks, but it does not have a mechanism to keep track of bugs. It has a large notes area where we embed a Google spreadsheet to do that. The tool is very easy to set up and run. It comes with a Gantt chart, Facebook-like wall, and versioned document upload facility. Besides, it has a neat bucketed structure which helps to section out the work.
I agree with the previous post that you should be careful about the shelf life of such tools. We have been using this tool for a while now. It is very stable, and the company is responsive to our feature requests, so I am hoping they will stay on...