I handle projects for several companies, I assume that I would set up an organization for each company and the boards would be the projects for each. Along these lines are there limitations on the number of organizations I can create, or on the number of boards under each organization?
From this Trello blog article about Trello Gold regarding new features (see questions near bottom):
You can still use Trello for free and enjoy unlimited boards, organizations, cards, and no usage restrictions, with or without Trello Gold. You can invite an unlimited number of people to your boards and organizations for free.