Up to what version of CiviCRM is secure to upgrade on a Drupal 6 site?
Pete is right that even recent versions of CiviCRM (certainly in the 4.6.x series) work with Drupal 6 sites.  The "no longer officially supports" issue is that the core team won't go out of their way to make D6-specific fixes.

That said, I have encountered problems with new installations on Drupal 6, but this has been for testing--why else would someone build a new site on Drupal 6?