I used to backup my photos on Flickr, but Flickr is awful for backups. You can't upload lengthy videos, you can't backup your raw files, retrieving your whole collection back from Flickr is extremely painful, etc...
So recently I'm switching to Google Drive for my backup needs.
I know a lot of people who also used flickr primarily as a backup solution. Sharing their photos with strangers on the Internet was always a secondary motivation.
This may, at least in part, explain flickr's gradual decline. In the age of cheap 3TB hard drives, 64GB SD cards, and cloud backup solutions, flickr seems a little old-hat.
I use it as a backup, and catalog. I still have my photos on my hard drive, but I know if it dies they'll be on flickr still. This was more important to me before I had dropbox.
Flickr also serves as a great cataloging tool. It's quicker for me to find a photo by tag on flickr than to find it locally.
So recently I'm switching to Google Drive for my backup needs.