Here's an example to show the distribution of random numbers as an image. Credit to Hayley Watson at the mt_rand page for the original comparison between rand and mt_rand.

rand is red, mt_rand is green and openssl_random_pseudo_bytes is blue.

NOTE: This is only a basic representation of the distribution of the data. Has nothing to do with the strength of the algorithms or their reliability.

<?php
header("Content-type: image/png");
$sizex=800;
$sizey=800;

$img = imagecreatetruecolor(3 * $sizex,$sizey);
$r = imagecolorallocate($img,255, 0, 0);
$g = imagecolorallocate($img,0, 255, 0);
$b = imagecolorallocate($img,0, 0, 255);
imagefilledrectangle($img, 0, 0, 3 * $sizex, $sizey, imagecolorallocate($img, 255, 255, 255));

$p = 0;
for($i=0; $i < 100000; $i++) {
    $np = rand(0,$sizex);
    imagesetpixel($img, $p, $np, $r);
    $p = $np;
}

$p = 0;
for($i=0; $i < 100000; $i++) {
    $np = mt_rand(0,$sizex);
    imagesetpixel($img, $p + $sizex, $np, $g);
    $p = $np;
}

$p = 0;
for($i=0; $i < 100000; $i++) {
    $np = floor($sizex*(hexdec(bin2hex(openssl_random_pseudo_bytes(4)))/0xffffffff));
    imagesetpixel($img, $p + (2*$sizex), $np, $b);
    $p = $np;
}

imagepng($img);
imagedestroy($img);
?>

[Editor's note: the bug has been fixed as of PHP 5.4.44, 5.5.28 and PHP 5.6.12]

Until PHP 5.6 openssl_random_pseudo_bytes() did NOT use a "cryptographically strong algorithm"! 
See bug report https://bugs.php.net/bug.php?id=70014 and the corresponding source code at https://github.com/php/php-src/blob/php-5.6.10/ext/openssl/openssl.c#L5408

Another replacement for rand() using OpenSSL.

Note that a solution where the result is truncated using the modulo operator ( % ) is not cryptographically secure, as the generated numbers are not equally distributed, i.e. some numbers may occur more often than others.

A better solution than using the modulo operator is to drop the result if it is too large and generate a new one.

<?php
function crypto_rand_secure($min, $max) {
        $range = $max - $min;
        if ($range == 0) return $min; // not so random...
        $log = log($range, 2);
        $bytes = (int) ($log / 8) + 1; // length in bytes
        $bits = (int) $log + 1; // length in bits
        $filter = (int) (1 << $bits) - 1; // set all lower bits to 1
        do {
            $rnd = hexdec(bin2hex(openssl_random_pseudo_bytes($bytes, $s)));
            $rnd = $rnd & $filter; // discard irrelevant bits
        } while ($rnd >= $range);
        return $min + $rnd;
}
?>

Getting an integer value from a given range with an even distribution:

This function I created to solve the problem of modulo results causing overlap of ranged results (which gave an uneven distribution).

What I mean for those not as familiar with the problem: 

Using bytes for base 256 (base 16) and attempting to find a value in a range of values that may be for example 10-20 (a spread of 11) will not divide evenly, so values (using mod) will overlap and give more priority to some numbers than others.

Instead of calculating based on byte values, I used the byte values as keys to sort. This is very fast, and does not require large multiplications of data space that easily go over the value of Max Int.

Additionally: To make the user-supplied arguments not care about order I am using a handy swap function I found in the wild in conjunction with my function below.

// swap function

function swap(&$a,&$b) { list($a,$b)=array($b,$a); } // swap 2 variables-- no temp variable needed!

// function to get a random value within a given range of integers
    
function get_secure_random_ranged_value($max=99, $min=0) // handles 1 or 2 arguments, order does not matter
{
    $sortarray = array();
    $lo = (int)$min; 
    $hi = (int)$max;
    if ($lo > $hi) swap($lo,$hi); 
    $data_range = abs($hi - $lo) + 1; // +1 includes both the lowest 'zero' value and highest value of range
    $bytes_per_key = 4; // Max: ffff hex = 4,294,967,296 dec (over 4 billion) -- large span of random values covers massive datasets
    $num_bytes = $data_range * $bytes_per_key; 
    $byte_string = (bin2hex(openssl_random_pseudo_bytes($num_bytes))); // only one call needed to get string of bytes
    $byte_blocksize = $bytes_per_key << 1; // shift multiply by 2 since a byte is 2 characters wide
    
    while ($key = substr($byte_string,0,$byte_blocksize)) { // get next byte block from string
        $byte_string = substr($byte_string,$byte_blocksize); // remove selected byte block from string
        $sortarray[]=$key; // populate the array with keys temporarily as array values
    } 
        
    $sortarray = array_flip($sortarray); // swap to use the byte values as keys 
    ksort($sortarray); // randomize by keys
    return array_shift($sortarray) + $lo; // grab top value from array and add it to the lowest value in the range    
} 

//
// example getting values from 0 to 21:
//
    
for ($i=1;$i<=10;$i++) { $rnd = get_secure_random_ranged_value(21); echo "-> result: ".($rnd)." <br />\n";  } 

//
// example getting values from 14 to 21:
//

for ($i=1;$i<=10;$i++) { $rnd = get_secure_random_ranged_value(14,21); echo "-> result: ".($rnd)." <br />\n";  } 

//
// sample results from 14-21
//

-> result: 14
-> result: 18
-> result: 20
-> result: 15
-> result: 20
-> result: 16
-> result: 21
-> result: 15
-> result: 16
-> result: 17

FYI, openssl_random_pseudo_bytes() can be incredibly slow under Windows, to the point of being unusable.  It frequently times out (>30 seconds execution time) on several Windows machines of mine.

Apparently, it's a known problem with OpenSSL (not PHP specifically).

See: http://www.google.com/search?q=openssl_random_pseudo_bytes+slow

If you don't have this function but you do have OpenSSL installed, you can always fake it:

<?php
    function openssl_random_pseudo_bytes($length) {
        $length_n = (int) $length; // shell injection is no fun
        $handle = popen("/usr/bin/openssl rand $length_n", "r");
        $data = stream_get_contents($handle);
        pclose($handle);
        return $data;
    }
?>

Remember to request at very least 8 bytes of entropy, ideally 32 or 64, to avoid possible theorical bruteforce attacks.

After the fix of insecure number generation here:

http://cve.mitre.org/cgi-bin/cvename.cgi?name=CVE-2015-8867

This function as well as the text here needs an update. I believe this function is safe to use in FIPS compliant apps as well as it now used RAND_bytes instead of  the insecure RAND_pseudo_bytes().