I would think that the best way to build a TEAM with true team spirit would be to start with yourself!
If you are the leader of a TEAM, you should teach your TEAM to do what you do. Team spirit has to start with ones self. You have to dig deep with-in yourself and find your good points and try and find people who have the same goodness in them as you do. People who are working toward a common goal, would work well together to achieve such a goal.
I hope this helps!