You need to use date_create() before using date_format(). This is because date_format() expects a DateTime object as the first parameter.
$date = date_create($row['date']);
echo date_format($date, 'd/m/Y');
Another way to do the same thing:
$dt = new DateTime('2012-02-10');
echo $dt->format('d/m/Y');
For the PHP 5.4 users out there it can be simplified to:
echo (new DateTime('2012-02-10'))->format('d/m/Y');
edit
To comment on the alternative solutions provided, they can be simplified to:
echo date('d/m/Y', strtotime($row['date']));
Just keep in mind that they do not account for daylight savings time or timezones like DateTime does.