Linear stories

Conventional stories are, for the most part, linear. While events might be told out of order the intention is that you would start reading at page 1 and read each page in order to reach the end.

Critically, the reader doesn't get to make any choices that affect the narrative. Those of you who skip to the end of a whodunnit are the exception. Linear stories are not "games" in most cases, and are often categorised as Kinetic Novels when art is added with an engine like Ren'Py.

These structures are often referred to as narrative arcs. Much more detailed information about these structures can be found online. Here they are presented in brief, mainly for reference and to contrast with branching structures presented later.

A beginning, a middle, and an end

Graph of beginning, middle, and end

This is probably the first structure children are taught. Often without more explanation of exactly what should go where or why.

Three act play

Graph of act 1 setup, act 2 confrontation, and act 3 resolution
Act 1:
The first act introduces the characters, their world, and their relationships. Something happens which challenges the main character (the protagonist) and their initial attempts to deal with it leads to a dramatic situation that ends the first act.
Act 2:
In attempting to deal with the events of act 1 the protagonist finds themselves in an ever worsening situation. They must develop themselves to resolve the situation, a character arc, often learning from outside sources.
Act 3:
The drama is brought to a climax, the plot (and sub plots) are resolved, and the characters have a new sense of themselves.
See: Wikipedia: Three Act Structure  

The Hero's Journey

Graph of the Hero's Journey

The Hero's Journey has a number of different interpretations that differ in the number of steps. In the diagram above the steps are coloured in the same way as the overarching acts. Analyses of classical stories and modern films (such as The Lord of the Rings or Star Wars) can be found online.

The structure is often presented as a loop, implying further journeys for the hero lie ahead in the next book or the sequel. Many of the patterns presented here can be cascaded: each box can contain other patterns.

See: Wikipedia: Hero's Journey