How do you create a .gz file using PHP?

Simple one liner with gzencode():

gzencode(file_get_contents($file_name));

The other answers here load the entire file into memory during compression, which will cause 'out of memory' errors on large files. The function below should be more reliable on large files as it reads and writes files in 512kb chunks.

/**
 * GZIPs a file on disk (appending .gz to the name)
 *
 * From http://stackoverflow.com/questions/6073397/how-do-you-create-a-gz-file-using-php
 * Based on function by Kioob at:
 * http://www.php.net/manual/en/function.gzwrite.php#34955
 * 
 * @param string $source Path to file that should be compressed
 * @param integer $level GZIP compression level (default: 9)
 * @return string New filename (with .gz appended) if success, or false if operation fails
 */
function gzCompressFile($source, $level = 9){ 
    $dest = $source . '.gz'; 
    $mode = 'wb' . $level; 
    $error = false; 
    if ($fp_out = gzopen($dest, $mode)) { 
        if ($fp_in = fopen($source,'rb')) { 
            while (!feof($fp_in)) 
                gzwrite($fp_out, fread($fp_in, 1024 * 512)); 
            fclose($fp_in); 
        } else {
            $error = true; 
        }
        gzclose($fp_out); 
    } else {
        $error = true; 
    }
    if ($error)
        return false; 
    else
        return $dest; 
} 

This code does the trick

// Name of the file we're compressing
$file = "test.txt";

// Name of the gz file we're creating
$gzfile = "test.gz";

// Open the gz file (w9 is the highest compression)
$fp = gzopen ($gzfile, 'w9');

// Compress the file
gzwrite ($fp, file_get_contents($file));

// Close the gz file and we're done
gzclose($fp);

Also, you could use php's wrappers, the compression ones. With a minimal change in the code you would be able to switch between gzip, bzip2 or zip.

$input = "test.txt";
$output = $input.".gz";

file_put_contents("compress.zlib://$output", file_get_contents($input));

change compress.zlib:// to compress.zip:// for zip compression (see comment to this answer about zip compression), or to compress.bzip2:// to bzip2 compression.