Is there any good web app for communicating and sharing files privately with a group, preferably free?
I already know about Backpack and Glasscubes, but they are not free.
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Yahoo! Groups seems like it would fit your requirements.
I use Dropbox. It's excellent.
Dropbox as mentioned is great for file sharing.
For other communication and project management, we're using Comindwork. It has some basic file sharing as well.
I like Skydrive at http://skydrive.live.com it has 25GB, Office docs can be viewed and edited online, photos can be presented in slideshow, and folders with many files can be downloaded at once in one zip file.
Also, you can have folders shared privately with as many people you like, delimitted by the email. All you need is a WindowsLiveID, wich you have if you use hotmail.