The Berkeley Electronic Press offers an electronic subscription-based system for their journals. Look at the B.E. Journals in Theoretical Economics. Here you submit to all four journals at once and your paper gets accepted to one with the highest quality rating that the editors decide is appropriate for your paper.
NAJ Economics is Not A Journal but offers reviews of economics papers. One cannot submit papers but a strong rotating editorial board just finds papers freely available on the internet and post reviews of those they feel are worthy. From the FAQ:
The purpose of NAJ Economics is to work towards replacing the existing commercial system of scientific publication. Because papers published in printed journals are less available than working papers, which are freely available on the Internet, publication in the traditional sense inhibits scientific communication. It also generates additional costs as most printed journals charge high subscription fees, in particular to libraries. However, it does serve the useful purpose of certifying the scientific quality of published work. It also assures that articles remain available regardless of the idiosyncrasies of individual websites and links. Our immediate goal is to provide some of the useful certification functions of current journals at a negligible cost by reviewing papers that we think have substantial merit.I have some quibbles about the service. Without submissions a lesser known author might have trouble getting his paper reviewed. The editors will have a nightmare keeping links up to date, especially since they seem to link to papers on people's homepages. They also don't have the ability to force improvements in the papers they review the way a journal can.
But perhaps in this age of the internet one needs to separate the refereeing and distribution aspects of a journal. NAJEcon is an interesting step in that direction.