A few weeks ago, I suggested using Flickr to back-up the photos on your Android device. I still think Flickr is a great service and with 1 TB of storage, it's hard to beat!
Recently, Google has announced Google Photos and Google's offer is a tad bit better.
Google offers unlimited free storage for high quality photos and HD videos. It's easy to add the app to all of your devices, including your computer. Sharing photos is a snap. It offers some pretty cool photo editing tools, too (including piecing overlapping photos together to make one big panoramic view!) It will even organize photos automatically.
My favorite feature is the automatic photo back-up from the computer, phone, or other device.