All of the following form radiolucent stones except:
Xanthine
Cysteine
Allopurinol
Orotic acid
Plain radiograph 
Calcium-containing stones are radiopaque: 

Calcium oxalate +/- calcium phosphate 
Struvite (triple phosphate) - usually opaque, but variable 
Pure calcium phosphate 

Lucent stones include: 

Uric acid 
Cystine
Medication (indinavir is best known) stones 
Pure matrix stones (although may have a radiodense rim or centre) 

Key Point:
Cysteine and Cystine are different amino acids.