For those of you worried about Photobucket, you can attach and insert photos into posts for your stories and such. It's free!!
How To: Attach and Insert Photos into Posts
http://www.carls-sims-4-guide.com/forum/index.php?topic=26583.msg443597#msg443597Also, like others have suggested Imgur.com is an alternative.
Photo Sharing Using Imgur.com (How to Use Imgur)
http://www.carls-sims-4-guide.com/forum/index.php?topic=22892.msg403214#msg403214Their service is free, and it sounds like there is no storage limit per user. There are limits to size of files uploaded.
Still images cannot be larger than 20MB
GIF's images cannot be larger than 200MB
It maybe worth considering using a blog site to store and share your images. Blogs can be free, or if you want to add a domain name for $3. a month up to $25 a month. - See link below for more pricing details:
All WordPress.com blogs come with 3 GB of space for uploaded files and images (free)
https://wordpress.com/pricing/Google's blogger.com (Free) has unlimited storage with photos on Blogger if you choose the "Unlimited High Quality Picture" option. It doesn't count towards your 15GB!
https://www.blogger.comGoogle Drive has 15GB storage limit, however it's shared storage. Meaning that the 15GB of space can include space for photos, Music, video, other files, etc.
https://www.google.com/drive/I've put this post together in hopes that it helps members know there's cheaper alternatives out there.
I'm sorry that it won't help backup the photos from Photobucket, but the suggestions above may help going forward.