I use Flickr. Its free for a limited size version.
Under 'share pictures' it has a link to paste into HTML but also has links to paste into bulletin boards which is what these are. When writing a post on here, don't use the picture button just paste the code straight from your hosting page.
I would imagine photobucket and picassa have the same thing. I haven't used the galleries on this site.
Update
Just looked at picasa and it doesn't look like it provides code.
Photobucket does, its in Links on the right side of any picture view. You need the img code.