I imagine what you need to do is set up a construct to hold the dates you are interested in and either use that in your query or post processing the query data. For example:

<?php
$query=mysql_query("SELECT date,COUNT(*) as num FROM downloads WHERE prjID='".$_GET['id']."' GROUP BY date ORDER BY date ASC");
$num=mysql_num_rows($query);

// Get the first and last dates in the result set
$firstRow = mysql_result($query, 0);
$lastRow = mysql_result($query, $num-1);

// Now make thos the begin and end dates
$beginDate = new DateTime(strtotime($firstRow['date']));
$endDate = new DateTime(strtotime($lastRow['date']));
$currentDate = $beginDate;
$interestingDates = array();

// Populate our interestingDates array with all counts set to 0
while ($currentDate <= $endDate){
    $interestingDates[$currentDate->format('d.m.Y')] = 0;
    $currentDate->add(new DateInterval('P1D'));
}

// Reset the data result for looping over
mysql_data_seek($query,0);
while($row=mysql_fetch_array($query)){
    // Go ahead and format the string
    $formatedString = date("d.m.Y", strtotime($row['date']));

    // If the string is in our interestingDates array, update the count
    if (array_key_exists($formatedString, $interestingDates)){
        $interestingDates[$formatedString] = $row['num'];
    }
}

// Print it out
foreach ($interestingDates as $key=>$value){
    print "$key - $value\n";
}

NOTE 1: mysql_query is deprecated as of PHP 5.5.0 and will be removed in the future. Pleasue use another API - I recommend pdo_mysql.

NOTE 2: The current query is not parameterized. Using PDO, this would perhaps look like:

$sth = $dbh->prepare('SELECT date,COUNT(*) as num FROM downloads WHERE prjID= :prjID GROUP BY date ORDER BY date ASC');
$sth->bindParam(':prjID', $_GET['id'], PDO::PARAM_INT);
$sth->execute();

Disclaimer - I haven't actually run this code, I just wrote it off the top of my head. You might need to test/debug it.

Assuming you have data for all dates, just not for a particular id, you can do a condition sum:

SELECT date, sum(case when prjID='".$_GET['id']."' then 1 else 0 end) as num
FROM downloads
GROUP BY date
ORDER BY date ASC

WARNING! It's a very bad style to do it in SQL, but if you want -- you can :)

http://sqlfiddle.com/#!2/b491a/1/0

SELECT dynamic_date AS date, COUNT(downloads.date) AS num FROM (
    SELECT DATE_ADD(start, INTERVAL i - 1 DAY) AS dynamic_date, prjID FROM
      (
        SELECT @i := @i + 1 AS i FROM 
        (SELECT 0 UNION SELECT 1 UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9) t1,
        (SELECT 0 UNION SELECT 1 UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9) t2,
        (SELECT 0 UNION SELECT 1 UNION SELECT 2 UNION SELECT 3 UNION SELECT 4 UNION SELECT 5 UNION SELECT 6 UNION SELECT 7 UNION SELECT 8 UNION SELECT 9) t3,
        (SELECT @i:=0) init
      ) i_sequence,
      (SELECT MIN(date) start, MAX(date) finish, prjID FROM downloads WHERE prjID=5 GROUP BY prjID) minmax
    WHERE DATE_ADD(start, INTERVAL i - 1 DAY) <= finish
) date_sequence
LEFT JOIN downloads ON dynamic_date = downloads.date and downloads.prjID=date_sequence.prjID
GROUP BY dynamic_date
;