This topic has been briefly discussed in the page “Social Software”. Indeed, the archiving and storing features are paramount for social software. They are also paramount for photography and the choice is immense.
Cloud based solution are trendy, and you should read the terms and conditions of the provider you want to buy from, should you have any privacy question. Cloud is more secured, more agile and deliver a much better experience. It is difficult for me to recommend anything else even if, again, it is worthwhile reading all the details of the contract.
Dropbox, Adobe, Google Drive/Photos, Microsoft One Drive/Photos, Amazon Premium Services, Apple iCloud are the usual suspects but there are much more. Many Telecom companies also propose now local cloud solutions if you want your images to be stored and managed in your home countries.
It is also good practise to segment the following:
- Storing for “frequent” usage of images
- Archiving for back-up
Both topics are quite different and having 2 providers can make sense.
In theory, you should go for the cheapest/more secure one for archiving. It does not have to be a service dedicated to images or photography by the way. And you should go for a provider well integrated with your photo editing tools, or publishing tools when it comes to storing images that you are going to work at regularly.
Dropbox, Microsoft Onedrive can be good candidates for the former (archiving). Adobe is supposed to be a good tool for the latter.