“To maintain your independence you must always be needed and wanted. The more you are relied on, the more freedom you have. Make people depend on you.
Obviously no one is indispensable but I have found that my supervisor/manager really valued my services when they found out I was a Go to person. This is not to be confused with a Go For It person who does everything under the sun including menial tasks such as picking up flowers for his wife.
Rather it is making yourself the first one to volunteer for tasks and especially the ones others are reluctant to take on. This builds trust and also allows management to see what you are capable of.
And I do agree that the more you are relied on, the more freedom you have. I got to be involved in projects and tasks that were very exciting because others did depend on me. On most performance evaluation forms there is usually an area that asks about how reliable and dependable you are. If you rate high on this part it will go a long way to make you invaluable to your superiors and to the organization as a whole.