– ease of accessing for end users (this is the most important, because if you have end users who aren’t tech savvy, then having them have to do anything beyond point and click isn’t going to work (e.g. some sites require you first to create an account before being able to view others’ photos)

– easy of uploading: Ideally you want to be able to upload photos just by locating them and putting them up, and not having to resize them first to dimensions acceptable to the site hosting service.

– number of photos/amount of storage: some services are free but limit considerably the number of photos you put up, and amount of storage you use for these.

– advertising: I don’t particularly care if there is advertising on the site along with my photos, but of course it’s ideal if there isn’t. I used to use Ringo, but then noticed that some of the ads that appeared below my pictures were not appropriate (I didn’t really want a link to “meet hotties tonight!” appearing along with my photos, especially when I was using the site to share photos of schools with my teacher education students!!).

– given that I already use Gmail along with a number of other Google tools, it is really convenient to have my photo sharing be packaged with this.
– option to be able to share photos publicly (with anyone) or privately (for close friends, relatives, or any other select group).

A good resource for info on other photo sharing sites can be found on Wikipedia, as this seems to be kept up to date with a list of current ones. See:
http://en.wikipedia.org/wiki/Photo_sharing#Online_photo_sharing_websites

I’d be interested in hearing from others about your criteria for selecting photo sharing sites and which you prefer.