The files directive is used to include files containing classes, check [documentation][1].
You could include the file in the .module file.

    require_once __DIR__ . '/includes/blocks.inc';

**Edit**: Included the other solutions added by @Beebee and @Jimajamma in the answer:

    require_once  drupal_get_path('module', 'mymodulename') . '/includes/blocks.inc';
    module_load_include('inc', 'MY_MODULE', 'FILE_NAME');
    // This method is including a file residing in the module folder not in a subdirectory.

  [1]: https://drupal.org/node/542202