How do you get disparate teams to work together successfully?

We all face challenges across organisations, as various teams often have different priorities and ways of working to each other. Yet the need from the organisation’s perspective is a smooth flow of work across teams, in order to achieve desired results. Sometimes the individual teams may not appreciate these overall goals, or see their own priorities as more important. So we need to ensure that all teams and individuals understand the overall requirements and are then working to meet these collectively - this goes across eg. Service Desks and techn9ical support teams, project and operations teams, Devops and ITSM/ITOM teams. 

What do you think - what’s your experience of getting this to work? How can we improve collaboration and shared goals..?