There is a Microsoft application called 'Project' that is designed for this - I don't know much about it but it's web based so it should cover the cross platform aspect.
I hate recommending MS products but apparently this is a pretty good application.
If you don't like the idea of an MS solution, there's another web based product called Basecamp.
http://www.basecamphq.com/indexp.php
Ruby on rails, I believe.