Today I needed to add a class to a Drupal 7 region and found the lovely template_preprocess_region() function to do the dirty work for me. With this function, you can easily add any class to your regions with the code below.
In a nutshell, you find the region you want to add the class to and then append your class onto the end of the classes_array variable.
function MYTHEME_preprocess_region(&$variables) {
// Run a switch statement to find the correct region we want to add a new class to.switch($variables['region']) {
case 'left_sidebar':
// Once we've discovered the correct region, add our new class to the classes_array.$variables['classes_array'][] = 'blue';
break;
}}