Treat your team members as people and you will develop true team spirit. Most company structures are based on the premise that people can't be trusted. People are told not only what to do, but how to do it. A detailed reporting system ensures that every activity is tightly monitored. Managing people with the expectation that they will be responsible and do a good job is empowering and allows you to flatten your organization.
Accountability provides the balance to offset reduced supervision.
Take a hard look at how you treat different categories of employees. From the parking lot to the office to how you travel, examine everything from the eyes of a typical team member and find out if it supports a feeling of community or a feeling of hierarchy. Teams must exist for a reason. Make sure they know why they exist and what they must accomplish. They should know how their goals tie into the organization's high level strategic and business goals.