I must admit that I use several file sharing / online storage locations for my work. Together they cover my varied tasks: photography - OneDrive, writing - DropBox. I also use Google Drive to share articles with bloggers should they not have Dropbox or OneDrive.
All are free to use with the option to upgrade to paid versions if you really need more space than they already provide. I share my files around to keep within the (generous) limits and have the added bonus of having a choice when it comes to sharing files with other people.
Save your Word document (or any document, video, image, audio file) to Dropbox and you have access to it from any computer with internet. It's is easy to use, whether you use the app or desktop versions, and the screen layout is neatly organised - much more so than I am.
Another added bonus - you can easily sync Scrivener files to Dropbox (I like easy).
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Dropbox keeps your files stored in one easily organised area for you to access across devices and across locations. All you need is an account and internet access.