Dropbox lives on your desktop as a virtual folder. You can drag and drop files into your Dropbox and they'll appear on all of your devices. You also have the option to store files in a public folder so you can easily share them with a simple download link.
Price: Free (iOS, Android, Mac & PC, Web)
Google Drive is an online productivity suite that can be accessed with any device that's connected to the internet, either through an app or on the web. You can share and collaborate on documents and presentations, and it's great when multiple people need to poke around a file at the same time, as you can always see who else is viewing or editing a document.
Price: Free (iOS, Android, Web)
OneDrive is a great place to store all of your documents, photos, and videos, and you get 15 GB of free storage when you sign up. Since OneDrive is a Microsoft service, you'll always know that your files will play nicely with other Office apps, so you don't have to worry about if a document will open in Word or not.
Price: Free (iOS, Android, Windows Phone, Web)