General Deterioration:
* Run-down
* Shabby
* Worn-out
* Derelict
* Decrepit
* Battered
* Broken-down
* Neglected
More Severe Deterioration:
* Ruined
* Fallen into disrepair
* Crumbling
* Tumbledown
* Rickety
* In ruins
Figurative Usage:
* Faded (for something like a memory or a dream)
* Broken (for something like a spirit or a relationship)
The best synonym will depend on the context of your sentence.