Currently there are 34 free file hosting sites where you can store all kind of files you want and use it as a temporary file storage or as a place to share data with your friends.
Find File Host - free file hosts index
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If you run a free file host that isn't in Find File Host database, link back to us and send us all the details you can. At least name, url, maximum file size allowed, allowed file types, if registration is required or not and how long will teh uploaded file stay (when it'll be deleted). We'll be happy to add your site.
If you're moving big files over internet you might be more interested in free large file transfer sites