It is always recommended to read the release notes of the new release before updating, to make sure that the update doesn't break some of the current features.

The [release notes of Drupal 7.20](http://drupal.org/drupal-7.20-release-notes) mentions:

>The security fixes in this release change all image derivative URLs generated by Drupal to append a token as a query string. (As an example, links that previously pointed to a URL like http://example.com/sites/default/files/styles/thumbnail/public/field/image/example.png will now point to a URL like http://example.com/sites/default/files/styles/thumbnail/public/field/image/example.png?itok=zD_VaCaD.)

You can add the following line to your `settings.php` to get the images in the site working:

    $conf['image_allow_insecure_derivatives'] = TRUE;

but it would be as good as updating the core and not using the updates ;-)

Some useful links from the page:

 - [#1923336: Insert module doesn't work with Drupal
   7.20](http://drupal.org/node/1923336) - contains a working patch to solve this problem.
 - [#1923554: New anti-DoS measure breaks for some file
   URIs](http://drupal.org/node/1923554).
 - [#1923936: Responsive images and styles module doesn't work with
   Drupal 7.20](http://drupal.org/node/1923936)