Very simple stack in C
I see a number of things that may help you improve your code.

Use a stack pointer as a parameter

Right now, one can only have one stack at a time.  Worse, if one calls stack_init after some items have already been pushed onto the stack, there will be a memory leak.  An alternative scheme would be to have stack_init() return a pointer to a Stack and then use that as a parameter for all other calls.  That way, one could have multiple stacks simultaneously, making it that much more useful.

Initialize all values before use

In the stack_init routine, the head variable is initialized, but neither head-&gt;element nor head-&gt;next are initialized.  It's also probably a good idea to explicitly zero the size.  Although it's already zeroed at the moment because it's a file scope variable, if you follow the other advice on this list, you'll have to initialize it yourself.

Provide a way to free memory

Right now, the only way to free memory is to repeatedly call pop().  Unfortunately, the calling program has no way to know how many items are on the stack or to know when the stack is empty, so it's not going to be able to know how many times to do so.  I'd suggest providing at least an explicit isEmpty() call.

Provide a complete interface

At the moment, there isn't any way to actually use the stack except to call print_stack() which limits its usefulness in the extreme.  I'd suggest that adding a means of examining the top of the stack, as with a call to top() that returns the value for that item might be a good idea.

Don't access freed memory

These lines have a problem:

free(head);
head = head-&gt;next;


The problem is that after you've freed head, you dereference it to get the next pointer.  This is undefined behavior -- anything could happen and it probably won't be good!  Better would be to save a copy of the pointer, do your housekeeping and then free the copy like this:

struct Node* temp = head;
head = head-&gt;next;
free(temp);


Separate printing from data manipulation

There is no way at the moment to use pop without it printing something.  In a real program that use such a stack, that's unlikely to be the desired effect.  Better would be to have pop() just do what it needs to do and leave printing to the calling program.

Return something useful from functions

Most of your non-void functions return something useful, but pop always returns 0 which isn't very useful.

Encapsulate related data in a structure

The size and head elements are closely related items.  For that reason (and to accomodate suggestion #1 on this list), I'd recommend combining them into a struct instead like this:

struct Stack {
    struct Node* head;
    int size;
};


Use a typedef to simplify your code

If you use a typedef like this:

typedef struct {
    struct Node* head;
    int size;
} Stack;


the code can refer to simply Stack instead of struct Stack.  It's not necessary, but it does tend to make things a little easier to write and to read.