General Synonyms:
* Autonomy
* Self-reliance
* Freedom
* Self-determination
* Sovereignty
* Self-sufficiency
More Specific Synonyms:
* Political independence: Sovereignty, autonomy, self-governance, liberation.
* Personal independence: Self-reliance, self-sufficiency, autonomy, self-direction, self-empowerment.
* Financial independence: Self-sufficiency, financial freedom, economic independence, financial autonomy.
The best synonym for "independence" will depend on the specific context in which you are using the word.