A fascinating list of the 36 types of stories according to French Writer Georges Polti, posted on Futility Closet:
In 1916, after extensive study, French writer Georges Polti announced that all the stories in classical and modern literature could be reduced to 36 essential situations:
1. Supplication. The Persecutor accuses the Suppliant of wrongdoing, and the Power makes a judgment against the Suppliant.
2. Deliverance. The Unfortunate has caused a conflict, and the Threatener is to carry out justice, but the Rescuer saves the Unfortunate.
3. Crime pursued by vengeance. The Criminal commits a crime that will not see justice, so the Avenger seeks justice by punishing the Criminal.
4. Vengeance taken for kin upon kin. Two entities, the Guilty and the Avenging Kinsmen, are put into conflict over wrongdoing to the Victim, who is allied to both.
Kay Camden 
I don’t think there will ever be agreement on the official number of story types; I’ve also heard 20, 7, and 3. Personally, I’m sticking with 3, as I’m getting older, and it’s a nice, small number. :)
Three is much easier to handle, especially since I think a lot of stories are combinations of the above list.
Was it Ray Bradbury who said three types?
1. Man comes to town.
2. Man meets woman.
3. Man leaves town.
I haven’t disproved it yet.
And “Shane” is all three! :)