General:
* Shabby
* Worn
* Used
* Secondhand
* Battered
* Faded
* Tattered
* Dilapidated
* Run-down
* Decrepit
* Ragged
* Timeworn
* Well-used
* Well-loved (implies a positive aspect)
For clothing:
* Threadbare
* Frayed
* Patchy
* Moth-eaten
* Baggy
* Wrinkled
* Disheveled
* Dingy
For buildings:
* Derelict
* Neglected
* Distressed
* Crumbling
* Falling apart
* In disrepair
For furniture:
* Chipped
* Scratched
* Stained
* Scuffed
* Ripped
* Broken-down
More descriptive:
* Distressed (can imply intentional wear)
* Patched
* Rusted
* Dusty
* Soiled
* Grimy
* Grungy
* Salvaged
* Revived (implies something is being brought back from a worn state)
Figurative:
* Tarnished (for reputation or image)
* Diminished
* Eroded
* Worn thin (for patience or resources)
The best word to use depends on the specific context and the effect you want to achieve.