If you just need to find out if two files are identical, comparing file hashes can be inefficient, especially on large files.  There's no reason to read two whole files and do all the math if the second byte of each file is different.  If you don't need to store the hash value for later use, there may not be a need to calculate the hash value just to compare files.  This can be much faster:

<?php
define('READ_LEN', 4096);

if(files_identical('file1.txt', 'file2.txt'))
    echo 'files identical';
else
    echo 'files not identical';

//   pass two file names
//   returns TRUE if files are the same, FALSE otherwise
function files_identical($fn1, $fn2) {
    if(filetype($fn1) !== filetype($fn2))
        return FALSE;

    if(filesize($fn1) !== filesize($fn2))
        return FALSE;

    if(!$fp1 = fopen($fn1, 'rb'))
        return FALSE;

    if(!$fp2 = fopen($fn2, 'rb')) {
        fclose($fp1);
        return FALSE;
    }

    $same = TRUE;
    while (!feof($fp1) and !feof($fp2))
        if(fread($fp1, READ_LEN) !== fread($fp2, READ_LEN)) {
            $same = FALSE;
            break;
        }

    if(feof($fp1) !== feof($fp2))
        $same = FALSE;

    fclose($fp1);
    fclose($fp2);

    return $same;
}
?>

It's faster to use md5sum than openssl md5:

<?php
$begin = microtime(true);

$file_path = '../backup_file1.tar.gz';
$result = explode("  ", exec("md5sum $file_path"));
echo "Hash = ".$result[0]."<br />";

# Here 7 other big files (20-300 MB)

$end = microtime(true) - $begin;
echo "Time = $end";
# Time = 4.4475841522217 

#Method with openssl
# Time = 12.1463856900543
?>

About 3x faster

In response to using exec instead for performance (Nov 13 2007 post), It looks like the performance depends on the size of the file.  See the results below using the same script from the original post.  The first hash is with md5_file and the second is with openssl md5.

With a 1MB file:
Hash = df1555ec0c2d7fcad3a03770f9aa238a; time = 0.005006
Hash = df1555ec0c2d7fcad3a03770f9aa238a; time = 0.01498

With a 2MB file:

Hash = 4387904830a4245a8ab767e5937d722c; time = 0.010393
Hash = 4387904830a4245a8ab767e5937d722c; time = 0.016691

With a 10MB file:

Hash = b89f948e98f3a113dc13fdbd3bdb17ef; time = 0.241907
Hash = b89f948e98f3a113dc13fdbd3bdb17ef; time = 0.037597

Performance seems to change proportionally with the file size.  Judging from the previous post's default file name (.mov) he/she was probably dealing with a large file.  These are just quick tests and far from a perfect benchmark, but you might want to test your own files before assuming that the openssl solution is faster (ie, if working with small text files vs. movies, etc)