Good question, but many of us who have been around for a while use pbase. (www.pbase.com) The interface is a bit strange, but you'll easily get the hang of it. Best feature is NO ADVERTIZING and no irritating pop-ups. Basically make a "donation" to SLUG, the site owner. Permits ZIP uploads and has many user-defined options. His service is fairly reliable, more so now that he has started charging for the service (it was free and donations were voluntary for quite some time).
It is 24.95/year and they allow 1500 images. Once you join there is no advertising and I have been incredibly happy with their site and their customer service.