Here is a listing of the commonly accepted historical Shaolin sword forms. Note that not all of these are currently taught in Shaolin.

Shaolin Damocles sword form  
Shaolin Chou Gong sword form  
Shaolin Sou Feng sword form  
Shaolin 8 immortals sword form  
Shaolin fire dragon sword form  
Shaolin green dragon sword form  
Shaolin cloud and sunshine sword form  
Shaolin Long Quan sword form  
Shaolin Wu Tang sword form  
Shaolin dragon shape sword form  
Shaolin Shan Pan 8 immortals sword form  
Shaolin 7 stars sword form  
Shaolin Damocles sword form  
Shaolin dragon form sword form  
Shaolin shuttle forest sword form  
Shaolin green wind sword form  
Shaolin boy sword form  
Shaolin single broad sword form 1  
Shaolin green dragon broad sword form  
Shaolin clubs broad sword form  
Shaolin clubs broad sword form 2  
Shaolin black tiger broad sword form  
Shaolin 5 tigers and a flock of sheep broad sword form  
Shaolin swallow form broad sword form  
Shaolin 4 kinds broad sword form  
Shaolin wrapping head broad sword form  
Shaolin double broad sword form  
11 Southern Shaolin Temple double broad sword form  
Shaolin Chun Qiu big broad sword form  
Shaolin Chun Qiu big broad sword form 2  
Shaolin Pu broad sword form