Imageshack and Photobucket were both the go-to image hosts of the old-internet era, maybe circa 1999 - 2006. They're both terrible services nowadays: imageshack went paid-only for a while (is it still paid only?), and they told me they'd lock me out of all my images past about 100, unless I paid. Had to download several thousand of 'em, though like 137th Gebrig said, a bunch of my old images from 2004 or so got corrupted for no apparent reason. Photobucket got bought out by Newscorp and now appears basically unusable its so jam packed with adverts and "features".
To be honest I'd say the best solution is to locally host the images on your computer via the cloud, using a cloud service like Dropbox, Google Drive, OneDrive, or Amazon Drive. All have paid plans but they give a load of free space. I like them as I can use them as I would a file browser on my PC, just make folders for different projects. Then I can link the images I want directly from the folder to the net, and all my stuff is backed up
