You need to shuffle things around a little, read the first number outside of the loop and assign it to largest, then go into the loop and do your tests. It's also better to use a for loop when you know exactly how many times you're going to repeat. You also want to print largest at the end instead of number.
Code:
#include <stdio.h>
int main(void)
{
int number, largest;
int counter = 0;
printf( "Enter Number: " );
fflush(stdout);
scanf( "%d", &number );
largest = number;
for (counter = 0; counter < 10; counter++)
{
printf( "Enter Number: " );
fflush(stdout);
scanf( "%d", &number );
if ( number > largest )
largest = number;
}
printf( "Largest Number was: %d\n", largest );
return 0;
}