To know what cloud storage is best for you really need to know what you want. Do you want to store, sync, collaborate, backup? I have used all three of the following free storage options.
Dropbox, with 2 GB free storage, is promoted by many. The prime reason most give for preferring it is the ability to sync files. When you are on your laptop and you change a file it automagically changes that file on your desktop and all other devices. That is not always a good idea in my book. Yes, it gives you a mirror backup on all your devices but if you mistakenly delete a file or overwrite a good file it is gone on all your devices. If I am collaborating with a researcher and they change the file it is changed whether I think that was a smart idea or not. If you want to share files or collaborate you need to give the other person log on information. I'm not comfortable with that. I can attach it to an email instead. You can limit the folders they see.
Dropbox has an app for almost every device making logging on pretty much a no brainer. There are ways you can up your free Dropbox storage to 8 GB which involve giving out your friends' emails.
Windows SkyDrive gives you 25 GB free storage, no strings. It provides backup and makes your files available from another computer. You can chose which files your want to sync and which you don't. You can chose who you want to share with and which folders you share with them. You can provide a link to files you want others to see. Reviewers like to note is the 50 MB limit on file size. Check your files and see how many you have which are 50,000 KB. If you have a lot of large pictures saved in .tif that might be an issue. Otherwise you should be good to go.
Windows SkyDrive does not have an app for all your devices. You need to log in. Make it a favorite or a bookmark.
Amazon Cloud Drive gives you 5 GB free storage. If you buy an album during the promotion period you can get an additional 20 GB. Amazon wants you to buy music from them and store it on the cloud drive so it is available to you wherever you are. I did put some music there - music you buy from them does not count against your storage limit - but mostly my storage is genealogy files. That's really what it is, storage which you can access - no sharing, no sync, at least not yet. Apple, in its infinite wisdom, has withheld approving any app which accesses Amazon because, of course, they want you to buy music from them using iTunes. If you are using the storage for backup or to have files available to you from another computer then this is not an issue. It works for storage.
Google's cloud drive for the masses seems to be lost in space. You have long been able to collaborate on documents. Google has free photo sharing through Picasa. They made cloud storage available for the Google Apps customers but reviews were not exactly glowing.
Your computer manufacturer may also provide you with some free cloud storage. There are some other companies that provide a small amount of free storage.
Is it safe? The original file is still on your hard drive I hope and you do back that up, right?
Bottom line: there is free cloud storage out there. Chose the one that suits your needs. Or chose all of them. In theory you could have 58 GB free cloud storage that way.