Google Docs and Spreadsheets is somewhat like Basecamp, the service I used recently on a project and blogged about here last month.
The advantage of Googles service seems to be:
You can create documents online (rather than only uploading them)
You can edit with others real time online
You can export your files in a variety of formats.
While Basecamp allowed others to edit, it wasn't real-time - it was controlled by version numbers. You could, therefore, potentially edit something at the same time causing errors.
Also, My biggest difficulty with Basecamp is the way that it exports. I can't use a web based pdf maker that uses the URL because it is a password protected site. The formatting is lost when I copy it into an office document. And their only export option is xml which I don't have the software to translate into something more usable. It allows you to archive it on the site, which is good, but leaves me with no soft copy of the project. I can easily download the files that where shared and revised - it is the to-do lists, messages and such that are more problematic.
Google, on the other hand, uses files for all activities - to-do lists, contacts ect. It is not specifically formatted to be a project management software, yet can be adapted into that quite easily. I also like that Google allows you to publish the file to a web page or a blog.
To learn more: http://docs.google.com/support/?hl=en