The common idiom is using both:

typedef struct S { 
    int x; 
} S;

They are different definitions. To make the discussion clearer I will split the sentence:

struct S { 
    int x; 
};

typedef struct S S;

In the first line you are defining the identifier S within the struct name space (not in the C++ sense). You can use it and define variables or function arguments of the newly defined type by defining the type of the argument as struct S:

void f( struct S argument ); // struct is required here

The second line adds a type alias S in the global name space and thus allows you to just write:

void f( S argument ); // struct keyword no longer needed

Note that since both identifier name spaces are different, defining S both in the structs and global spaces is not an error, as it is not redefining the same identifier, but rather creating a different identifier in a different place.

To make the difference clearer:

typedef struct S { 
    int x; 
} T;

void S() { } // correct

//void T() {} // error: symbol T already defined as an alias to 'struct S'

You can define a function with the same name of the struct as the identifiers are kept in different spaces, but you cannot define a function with the same name as a typedef as those identifiers collide.

In C++, it is slightly different as the rules to locate a symbol have changed subtly. C++ still keeps the two different identifier spaces, but unlike in C, when you only define the symbol within the class identifier space, you are not required to provide the struct/class keyword:

 // C++
struct S { 
    int x; 
}; // S defined as a class

void f( S a ); // correct: struct is optional

What changes are the search rules, not where the identifiers are defined. The compiler will search the global identifier table and after S has not been found it will search for S within the class identifiers.

The code presented before behaves in the same way:

typedef struct S { 
    int x; 
} T;

void S() {} // correct [*]

//void T() {} // error: symbol T already defined as an alias to 'struct S'

After the definition of the S function in the second line, the struct S cannot be resolved automatically by the compiler, and to create an object or define an argument of that type you must fall back to including the struct keyword:

// previous code here...
int main() {
    S(); 
    struct S s;
}

My question is why typedef needs flight to be written a second time at the end of a block?

When you declare:

typedef struct flight{
    int number;
    int capacity;
    int passengers;
 }flight;

you actually declare two things:

• a new structure type struct flight
• a type alias name flight for struct flight.

The reason why the type alias name with typedef appears at the end of the declaration like for any ordinary declaration is because for historical reasons typedef was put in the same specifiers category as storage-class specifiers (like static or auto).

Note that you can just declare:

typedef struct {
    int number;
    int capacity;
    int passengers;
}flight;

without the tag name if you intend to only use the type identifier flight.

As Greg Hewgill said, the typedef means you no longer have to write struct all over the place. That not only saves keystrokes, it also can make the code cleaner since it provides a smidgen more abstraction.

Stuff like

typedef struct {
  int x, y;
} Point;

Point point_new(int x, int y)
{
  Point a;
  a.x = x;
  a.y = y;
  return a;
}

becomes cleaner when you don't need to see the "struct" keyword all over the place, it looks more as if there really is a type called "Point" in your language. Which, after the typedef, is the case I guess.

Also note that while your example (and mine) omitted naming the struct itself, actually naming it is also useful for when you want to provide an opaque type. Then you'd have code like this in the header, for instance:

typedef struct Point Point;

Point * point_new(int x, int y);

and then provide the struct definition in the implementation file:

struct Point
{
  int x, y;
};

Point * point_new(int x, int y)
{
  Point *p;
  if((p = malloc(sizeof *p)) != NULL)
  {
    p->x = x;
    p->y = y;
  }
  return p;
}

In this latter case, you cannot return the Point by value, since its definition is hidden from users of the header file. This is a technique used widely in GTK+, for instance.

UPDATE Note that there are also highly-regarded C projects where this use of typedef to hide struct is considered a bad idea, the Linux kernel is probably the most well-known such project. See Chapter 5 of The Linux Kernel CodingStyle document for Linus' angry words. :) My point is that the "should" in the question is perhaps not set in stone, after all.