It's an interesting concept. Depending on who you ask, the number of plot types varies greatly. When I was in grade school, I was taught there are three:
Man vs Man - conflict between people
Man vs Nature - conflict between a person and the world or environment (i.e., monster movies, or climbing a mountain)
Man vs Himself - internal conflict or struggle
It's the unique elements that make a story interesting and new, but all stories can be reduced down to one of these simple styles.
Other schools of thought extrapolate this basic framework and say there are seven:
Man vs Man
Man vs Nature
Man vs Environment
Man vs Machines and Technology
Man vs The Supernatural
Man vs Himself
Man vs God/Religion
I don't agree with this. All of those can be put into the three containers, although combinations are possible (and again, are what makes things interesting.) 'vs God/Religion', for instance, could be seen as 'vs Man' and/or 'vs Nature'.
Yet more categorizations count more types of plot, with themes such as:
Quest
Adventure
Pursuit
Rescue
Escape
Revenge
(and more.) This is from Ronald Tobias's
20 Master Plots. Again, while deeper studies may use this classification system to reveal intricate ideas of story construction, I see a lot of overlap between these.
or:
Deliverance
Crime Pursued by Vengeance
Vengeance taken for kindred upon kindred
Pursuit
Disaster
Falling Prey to Cruelty of Misfortune
Revolt
(and more.) Georges Polti's
The Thirty-Six Dramatic Situations.)