There is an issue tracking this problem on drupal.org - http://drupal.org/node/550428. There is a patch in comment number 49 for it, hope it helps.

In sites/all/modules/ckeditor/ckeditor.config.js, add the following line at line 11, just below CKEDITOR.editorConfig = function(config) {:

config.fillEmptyBlocks = false;

You can have a look at CKsource's documentation for more advanced uses of this function. Why config.ignoreEmptyParagraph = true; is not sufficient is beyond my understanding, though.

Have you tried setting the fillEmptyBlocks CKEditor setting to false? In WYSIWYG you would do this with a hook:

function base_wysiwyg_extras_wysiwyg_editor_settings_alter(&$settings, $context) {
  if ($context['profile']->editor == 'ckeditor') {
    $settings['fillEmptyBlocks'] = FALSE;
  }
}

There's probably a CKEditor module way too. If there's not, you can always add settings directly with a custom CKEditor settings js file.

Answer above fix this if you have a CKEditor module, but if you use WYSIWYG module you don't have that option (at least for now).

Here is how to override these settings with a module in CKEeditor in Drupal 7:

function YOURMODULENAME_wysiwyg_editor_settings_alter(&$settings, $context) {
  if($context['profile']->editor == 'ckeditor') {
    $settings['enterMode'] = 2; //<br />
    $settings['shiftEnterMode'] = 1; //<p>
  }
}

For TinyMCE here Drupal 7 - How to change p to br in CKEditor and TinyMCE.

There is a reason why the paragraph is the default: usually it's semantically more correct to use a <p> tag. I recommend in most cases to stick to the default and (if you don't like the whitespace) remove the margin on paragraphs using CSS.