General:
* Act
* Action
* Doing
* Performance
* Operation
* Achievement
* Exploit
* Feat
More specific:
* Good deed: Kindness, benevolence, charity, service
* Bad deed: Crime, offense, misdeed, transgression
* Legal deed: Document, instrument, contract
* Heroic deed: Bravery, valor, exploit, feat
The best synonym will depend on the specific meaning you want to convey.