I've heard imgur. But I don't know, the free options seem fewer these days. I guess none of the photo hosting sites have figured out any way to make money out of it, unless they charge membership fees.
Gosh - are they? I have some there, and quite a few of the photos on the church website are hosted there as the size restrictions on the site used to make it difficult to just upload them, in the past.
I have used Flickr for a long time - I started using it to keep a specific set of pictures there, linked to my own name rather than my LJ one, but have found it better than photobucket so it has become my default these days. It is free in the basic form - although I have a pro account there - I don't think it costs me much - I pay for it every year I think but can't honestly, remember.