Dropbox - this free App gives you 2 GB worth of free space when you sign up; however, you can increase your box size by inviting others to use the service. When you automatically save photos and videos, you can earn up to 3 GB. From personal experience, if you need to access files from Dropbox website, it is very easy to use.
Box - this free App gives you 5 GB worth of free space to store all of your pictures and files. This App has a Microsoft feel because many of the icons look like the familiar icons of Windows. Although very similar to Dropbox, it doesn't have the auto-upload feature for photos like the popular App.
What Apps do you use for file storage? I'm curious.