How to turn off Captcha for search?
For a block, the form_id should be: 


  search_block_form


and for a page:


  search_form


To easily find this information, install the Devel module:


  A suite of modules containing fun for module developers and themers


and use something like this in your theme's template.php file:

function myTheme_form_alter(&amp;$form, &amp;$form_state, $form_id)
{
    dpm($form);

}


This will show a hierarchical display of all forms on the page - you can then scroll quickly through the info to find what you need. Very handy for searching arrays.