First non-repeated character in a string in c
Alex, it looks quite efficient. There are some issues that I see:


gets should never be used. Use fgets (but note that you will have to strip the trailing \n)
define main at the end to avoid the need for a prototype for repeat_ch
declare repeat_ch as static
your limit does not work as i is not incremented.  But why not stop on
reading an empty string rather than limit the number of loops?
NULL is normally defined as (void *) 0 so comparing a char with NULL is
wrong.  The compiler will warn you of that.  Just use 0 or better '\0'


In repeat_ch


function name is inaccurate - function looks for a non-repeated char.
the two // comments are noisy (ie. don't tell reader anything)
array would be better sized 256
p should be const
for-loops would be better

for (const char *p=string; *p; ++p) {
    array[*p] += 1;
}
for (const char *p=string; *p; ++p) {
    if (array[*p] == 1) {
        return *p;
    }
}
return '\0';