I must admit I haven't used Photobucket in a while, it seemed to be keeping place with changes in other on-line services like google+,flickr & tumbler but I kind of backslide into just using blogger and flickr for my blog posts. It was once my first choice to add photos into my blogger posts! Ok that was almost a decade ago. I actually liked their idea of stories, but never got around to creating any. Anyway the display of photo and the uploads have had some significant updates, see the video below.
If you are new to storing your photos and videos on the web, and want a safe place to share a few (not everything) then a photobucket free account is a good place to start. Photobucket is a solid well thought out service, that has been around a fair while now and gives you one place to upload, edit, organise, share and print your digital photos, with the addition of an active community as well, albeit largely teenagers these days.