The Society's most notable private research project to date involves a "simulated Mars habitat" on Devon Island, an island in the Arctic with geography and weather conditions resembling some aspects of Mars. At this research station they have tested communication, command, scheduling, and scientific investigation techniques and approaches under simulated Mars conditions (for instance, each exit from the main habitat requires the wearing of a pseudo-spacesuit and a 20-minute prebreathing period, as would be necessary on Mars). At a cost of over 1 million US dollars, the society has demonstrated considerable fundraising and technical capabilities (though, of course, a small fraction of the billions of dollars required for an actual manned Mars mission).
The Mars Society has announced their next major project involves investigating the biological effects of extended exposure to centrifugally-generated Martian "gravity" on mice.
The Society's web site can be found at http://www.marssociety.org