You will find that most image hosts and image upload sites are free. However, they do impose restrictions on such things as the maximum upload size and monthly bandwidth usage. Still, it's a lot better than purchasing web hosting in order just to share images or to save on bandwidth for your existing web sites.
Most image hosts will often have the option to subscribe to a paid hosting service, which while still very inexpensive (a couple of dollars a month) can offer much more bandwidth and much less upload restrictions.
In most cases, the image upload site will often be supported by advertisements which allows them to offer everyone free image hosting.