There are a lot of options if you want to store your files online (in the cloud) for free (free as in money not necessarily freedom). I’ve put together a list of the services I’m aware of and have used myself but this list will not be exhaustive. You can use these services as an off-site backup or for an easy way to share your files with family and friends.
Some of these services such as Google Drive and Zoho are online office suites which enable you to actually create and edit documents in your web browser. Also some services such as Flickr and YouTube will only store certain file types, for example Flickr will only store photos and YouTube only videos.
This list is in no particular order.