Here are steps I use to update Drupal site code to the latest core and contrib module versions. This can be done via the command line using drush.
Doing 'drush up' (all by itself) is popular to update the site code but I don't use it. I suppose if you have a *very* simple site with very few modules that are all using pretty recent stable releases, then it is fine. But, I almost never deal with sites like that (except for simple test sites).
