A few years ago, if you wanted to store your photographs online and perhaps share them with friends, there really was only one game in town, and that was Flickr. It's the service that I grew up with, and even paid them money every year for the right to dump my photographs online. It was however rather more than a photo storage service, since it allowed people to network, share photographs, have discussions and so on - and indeed it still does exactly that, although now it's entirely free. It's still widely used by public library services to share photographs online, and the ability to quickly find images that you can use under a CC licence is still exceptional. It's still my 'go to' place to find images that I need to use.
There are however plenty of other services, such as the Apple iCloud Photo library. If you're an Apple user, then this is probably the service for you - you can back up the photographs that you've taken from your phone or tablet and make them instantly available.
Amazon Prime users can have unlimited space to upload their photographs, although if you're not a Prime user and want the service you can have it for a small annual fee.
Then we have Google photographs, which is the newest of the services. It's the one that I've particularly taken to, and have uploaded a fair number of my photographs already. You can keep them private or you can share them as you see fit, or perhaps create a folder of images that can be shared and keep everything else to yourself. Google photos is an astonishing service because it automatically indexes your photographs and makes them available for you in different collections. For example, I've got collections called 'beach' 'castle' 'dog' and so on. I can also search for things - 'mushroom' for example pulls up the single photograph in my collection that has them. It's not a perfect service, but it's very impressive indeed. Not only that, but Google photos also has an 'assistant' and this will automatically create collages, little movies, photos with special effects and so on. It's a perfect way to get some really interesting images with no work on your part at all.
I don't think there's a perfect service though - Flickr is great if you want to network with other people, iCloud is a winner if you're already an Apple user, Amazon ditto if you have Prime, and most people have a Google account. If pushed, I'd go for Google photos though, simply because of the search element, which is astonishing.