Image Coast is one such site.  Photo Bucket is another but some gals have complained about their photo policies.

When you do so, then the photo will have an URL which you can then copy and paste into the box for photo URLs when you start a post.

You can also choose a link from your own website which "hosts" your pictures.  As I look at it, your pictures are not actually hosted on your own site but on a different site - doesn't matter.  Once you copy the link into another webpage, that page will search for that link and put the picture where the URL is.

If you ever move, delete or change the name of the picture file, the webpages pointing to the old link won't be able to find the picture and will produce an appropriate error ("file not found" or something like that).  

I'm going to try it here using "copy image location" and then pasting in the "link URL" box below the "message" box