As of 5.0.0 the last parameter (count) is passed by reference (it is optional). So 2 choices :
1)passed not by reference - it's limit
2)passed by reference : the var is is_null() - all occurences are replaced the number is returned in "count", otoh if the var !is_null() -> use as limit.

Comments?

Why not simply add a further optional argument? This way You could even distinguish if less values where replaced.

Furthermore I'd like "limit" optionally to be an array, if "search" is of that type. This way You could specify different  replace limitations for differrent strings to be replaced.

Please correct me if I'm misled, but as far as I've seen in the sourcecode str_replace() is internally subdivided into two functions anyway, one "interface" and another function doing the "real work" for str_replace() and str_ireplace(). (BTW: Why not stri_replace()? Seems to be more apropriate..)
By implementing this feature we could easily have the same for str_ireplace() as well without much work and therfor avoid lots of usage of regular expressions.

In response to this, here's a simple function to replace the first one only (note that you could loop this function to replace more than one, but not all):

function str_replaceFirst($s,$r,$str)
{
	$l = strlen($str);
	$a = strpos($str,$s);
	$b = $a + strlen($s);
	$temp = substr($str,0,$a) . $r . substr($str,$b,($l-$b));
	return $temp;
}

How about this...

$count is passed by reference. Don't change this.
if (is_null($count)) {
   //replace all;
} elseif (floor($count) < 1) {
   //replace all;
} else {
   //replace first floor($count) occurences;
}
$count = number of actual replacements made

The only change from past behavior is that $count must be unset or made NULL before passing it by reference:

echo str_replace("o", "a", "moo", $count); // returns "maa"
echo str_replace("o", "a", "mooooo", $count); // returns "maaooo"
unset($count);
echo str_replace("o", "a", "mooooo", $count); // returns "maaaaa"

Thoughts?

On version 5.3.0 the 4th parameter, count, does not work when not passed 
by reference.

$count = 1;
echo str_replace("o", "a", "foo", $count); // returns "faa"

Even if it was working well, thought, this is not a good approach.

Use preg_replace() if you need this.

This is such a great idea! I can't believe it was suggested 10 years ago and no one added it =/

I would vote to add a str_replaceonce function where the $count arg specifies which occurrence in the string to change (negatives also.)

Changing the existing str_replace is something people can do on their own installation but I don't think it will be changed in the main code because it could break some existing software written in php.

Here's a workaround written in PHP that is 100% backward-compatible with str_replace: http://stackoverflow.com/a/11400172/526741

Are you kidding me? 13 years and "Won't fix"?

Simple code:
$bb_code = array('[b]','[/b]','[i]','[/i]','[u]','[/u]');
$html_code = array('<b>','</b>','<i>','</i>','<u>','</u>');
$html = str_replace($bb_code,$html_code,$edit);

Task: 
Allow to use bbcode only 2 times in whole article.

Good luck with preg_replace. 
I know it's possible, but when it comes to performance... yeah, right.

I'm too 'oldschool' to use "plugins" and "libraries" to replace BBCode, and much too old to waste my servertime for preg_replace.

After years of crappy programming and wasting resources it's time to start doing it right - as it was years ago.
So for God sake just add this simple limit, as you count replaces anyway...