The first seven . . .
1 - [wo]man vs. nature
2 - [wo]man vs. man
3 - [wo]man vs. the environment
4 - [wo]man vs. machines/technology
5 - [wo]man vs. the supernatural
6 - [wo]man vs. self
7 - [wo]man vs. god/religion
. . . can also be grouped together and put into another group of seven:
1. Overcoming the monster -- defeating some force which threatens...
e.g. most Hollywood movies; Star Wars, James Bond.
2. The Quest -- typically a group setoff in search of something and
(usually) find it. e.g. Watership Down, Pilgrim's Progress.
3. Journey and Return -- the hero journeys away from home to somewhere
different and finally comes back having experienced something and
maybe changed for the better. e.g. Wizard of Oz, Gullivers Travels.
4. Comedy - not neccesarily a funny plot. Some kind of
misunderstanding or ignorance is created that keeps parties apart
which is resolved towards the end bringing them back together. e.g.
Bridget Jones Diary, War and Peace.
5. Tragedy - Someone is tempted in some way, vanity, greed etc and
becomes increasingly desperate or trapped by their actions until at a
climax they usually die. Unless it's a Hollywood movie, when they
escape to a happy ending. e.g. Devils' Advocate, Hamlet.
6. Rebirth - hero is captured or oppressed and seems to be in a state
of living death until it seems all is lost when miraculously they are
freed. e.g. Snow White.
7. Rags to Riches - Cinderella.
And there are even more ways to classify them, but everything boils down to those few things.
--disclaimer: I ripped those examples and stuff from Google answers.