Raj Sisodia, the author of Firms of Endearment, talks about the trust in organizations. He mentions examples where organizations have moved from being low trust to high trust and the amount of effort involved in doing so. He makes a very important point when he says that organizations always expect the employees to be trustworthy but they do not always reciprocate the same. He also mentions building of trust as a long term goal as it takes time to build a trust in a large established organization.
I would like to add that Innovation will flourish in a high-trust organization. By its very nature, Innovation is a high risk game and one can never predict the outcome. People would be willing to take more risk if they can trust their teams, their managers and leadership. If they can trust them to share their ideas, if they can trust them to support them and share the credit if the idea take off finally, they will come forth and contribute in a much bigger way to the organization.
Interestingly, trust is big reciprocal trait. When you trust someone, you invite them to trust you. And unless one of you have hidden agendas, this can be the beginning of a trusting relationship.