You can back up your photos to roughly a billion different cloud services, but Amazon's latest Photos update might tempt you to give its Cloud Drive another shot. The v4.0 update offers more granular control over photo uploads, plus you can share photos more easily.
Here's the v4.0 changelog.
Upload any or all of your albums to Cloud Drive with Auto-Save
Play a slideshow of your favorite photo collections (Android 4.4 and up)
Share multiple photos to social networks, like Facebook and Twitter, and via email and SMS
Print your favorite photos directly from the app (Android 4.4 and up)
The Auto-Save improvement seems like the big deal this time around. Now when you turn on this feature, you can manage the folders on your device and control which ones are added to your Cloud Drive. Keep in mind Prime users have unlimited photo storage.
The app can also take advantage of Android 4.4 features to do full-screen slideshows and print from the device. Everyone now has the option of sharing multiple images to other services. The updated version should be live in the Play Store for everyone.