In dealing with the art and artifacts of Iraq we need to realize that we have two differant problems. The first is securing objects in possession of museums. The second is securing the archeological sites from which these objects come.
To secure the artifacts already in possession of museums there need to be an agreement amoung all nations that in the event that a country becomes unstable, other countries will step in and provide a safe haven for their collections. Of course upon re-establishment of order the collections should be returned to their countries of origin. Perhaps this could even be treated in a manner similar to the traveling exhibites often seen in museums. The real key to this is that it would be done before the onset of hosilities or invasion. The country in question should agree to it for no other reason than the preservation of their history. The bottom ine is that the collections should be moved, simply protecting them isn't feasible from a military perspective. Bombs and fire do not respect art.
The other problem is protecting the artifacts on the sites. Perhaps the best approach to this would be in helping raise the indigenous peoples standerd of living above that of subsistance. Education would also go a long way in helping people appreciate the historical value of things they see every day and take for granted.
Overall this is a complex problem which would take a lot money and understanding between different countries, cultures and religions to sort out.