A free photo backup app can keep your pictures safely backed up, synced across all of your devices, and clear up precious smartphone storage space, all for free. Apple and Google both have good default photo backup options, but there are other apps available with more free storage and additional features.
First, I'll go over the default options for Apple and Android devices before exploring some third-party apps that also work on these devices.
Default free photo backup app for iPhone & iPad
iCloud is the default photo backup app for iPhone and iPad, and is also accessible on computers at iCloud.com. iCloud has evolved a bit over the last few years and now provides photo backup (iCloud photo library), syncing of recent pictures across devices (Photo Stream), and sharing (iCloud photo sharing), along with device backups, mail, contacts, and more. iCloud comes with 5GB for free, which can be used up quickly, especially for users backing up multiple devices. More storage is available for purchase (see photo). Photos can only be uploaded when on wifi, and can be downloaded over cellular data if you choose.
iCloud is relatively easy to use and mostly works as advertised. However, it comes with a limited amount of free storage that is shared with other critical uses such as device backups, and isn't available on Android. Get more info on iCloud Photo here.
Default free photo backup app for Android
Google+ is the default free photo backup option for Android devices. The app can be set to automatically upload photos to your Google+ page, and kept private or shared publicly with your contacts. One of Google+'s interesting features is 'auto-awesome', a photo enhancement tool. Google+ comes with 15GB of storage for free, which is shared with your Google Drive and Gmail accounts. The app can be set to upload automatically over cellular or wifi only or just while your device is charging.
Google+ is a solid option with a good amount of free storage. Auto-awesome is a neat perk, but probably not enough of a reason to switch to Google+ from another service. If you already have a Gmail address and use a lot of Google services it's definitely worth a try. Get the app for Android, iPhone/iPad, or learn more about Google+ here.
Other free photo backup app options
Flickr is another free photo backup app with a crazy amount of free storage: 1TB (1,000GB). The app automatically uploads your new pictures and they can be viewed on other devices or the web. New uploads can be kept private or shared with other Flickr users. The app can be set to upload over cellular or wifi only. In the past the app was plagued with issues of photos not uploading automatically. That has been fixed, although I do notice occasional delays in photos being uploaded. If you take enough photos and videos to run out of free storage on one of the default options, then take a look at Flickr. Get the app for iPhone/iPad or Android, or get more info here.
Box is another popular cloud storage service that comes with 10GB of free storage. However, the app does not support automatic photo uploads, but it can be accomplished with the help of the great IFTTT app. Learn more about Box here.
I use Flickr to backup my entire photo library simply due to the vast amount of free storage it offers. I don't mind if my photos aren't uploaded within minutes of me taking them. This frees up my iCloud and Google Drive space for other uses, and my photos are still always backed up for free. If you don't take a ton of photos and videos you may get by with one of the default options just fine, but it may be a good idea to have your photos backed up in another place just in case something goes wrong. Flickr gives me this piece of mind at the bargain price of $0.