General:
* Release
* Loosen
* Open
* Detach
* Disconnect
* Untie
* Undo
* Unhook
More specific:
* Unbutton (for clothing)
* Unzip (for clothing)
* Unbuckle (for belts, buckles)
* Unscrew (for screws)
* Unclip (for clips)
* Unlatch (for latches)
* Unchain (for chains)
The best synonym to use will depend on the specific object being unfastened and the context of the sentence.