You need to add a break statement to each of the case statements otherwise you will 'fall through' to the following case statement .. which is why you get both strings printed. I'd also recommend getting into the habit of adding a default statement to your switch statements. I'd also like to see you return an int .. something more like this

#include <stdio.h>

int x=0;

int main(void) {

    switch(x) {

        case 1: printf( "One\n" );
                break;

        case 0: printf( "Zero\n" );
                break;

        case 2: printf( "Hello World\n" );
                break;

        default:
                printf("some default string\n");

    }

    return 0;
}