I started out with Photobucket.
Then I tried Flickr. When Flickr was in flux recently another member here mentioned SlickPic, so I signed up there.
And I stumbled on 500px, got a few photos there but they want you to pay, and with so many great free options I have let that account stay where it is.
I also found 1x. 1x is cool because it allows free usage, with an option to upgrade to a paid membership, but without pressure to do so. The photos you put up there are very well protected against someone snagging them for unauthorized use, something that many other sites claim but don't always deliver.
Right now I mostly use Flickr for my camera photos, and Photobucket to keep the "stolen" pictures I snag from the web to illustrate a point or be goofy when posting on internet forums, like this: