General:
* Damaged (the most direct and common)
* Deteriorated
* Devastated
* Ruined
* Worn
* Broken
* Spoiled
* Defective
* Impaired
* Injured
* Compromised
Specific to type of damage:
* Structural (for buildings, etc.)
* Cosmetic (superficial)
* Mechanical (for machines)
* Electrical
* Environmental
* Financial
* Reputational
Describing the severity:
* Extensive
* Severe
* Significant
* Minor
* Irreparable
* Reversible
Other:
* Collectable (for items that are damaged but still valuable)
* Salvageable (items that can be repaired or reused)
The best adjective to use will depend on the specific context of your writing.