How can I tell Drush in which folder should a module be copied? Is there a way to make Drush download modules into a specified folder besides sites/all/modules (e.g. sites/all/contrib, sites/all/core)?

If this makes a difference, I am using Drush 4.4.
You can default this to, for example, sites/all/modules/contrib, in your .drush/drushrc.php file.

$command_specific['dl'] = array('destination' =&gt; 'sites/all/modules/contrib'); 


Also note that you won't be able to exclude the 'modules' part of the path, as Drupal uses this to scan for modules.

There are 6 places this file can live:


  
  Drupal site folder (e.g. sites/{default|example.com}/drushrc.php).
  Drupal /drush and sites/all/drush folders, or the /drush folder in the directory above the Drupal root.
  In any location, as specified by the --config (-c) option.
  User's .drush folder (i.e. ~/.drush/drushrc.php).
  System wide configuration folder (e.g. /etc/drush/drushrc.php).
  Drush installation folder.