Thanks to discussion above I had it working in once, so perhaps one complete post can help others.
Using D6.11 + Views2

step 1
created folder: "form_alterations"
in "sites/all/modules/"

step 2
created file "form_alterations.info" in the folder from step 1
containing:

name = "Views exposed form alterations"
description = "Alter exsisting views exposed forms with a reset button."
core = "6.x"
version = "6.x-1.0"
core = "6.x"
project = "form_alterations"

step 3
created file "form_alterations.module" in the folder from step 2
containing:

<?php
/**
* Implementation of hook_form_alter().
*/
function form_alterations_form_alter(&$form, $form_state, $form_id) {
  if ($form_id == 'views_exposed_form') {
    $exposed_views = array('NAME_OF_VIEW', 'NAME_OF_VIEW2');
    if (in_array($form_state['view']->name, $exposed_views)) {
      $current_display = $form_state['view']->current_display;
      $form['reset'] = array(
        '#type' => 'markup',
        '#value' => '<input class="form-button" type="reset" 
value="Reset" onClick="javascript:window.location=\'/'. 
$form_state['view']->display[$current_display]->
display_options['path'] .'\';" />',
      );
    }
  }
}
?>

step 4
Replace

NAME_OF_VIEW

and

NAME_OF_VIEW2

with your view names.
Btw. To get the view name: open your view to edit it, the last variable in your URL should be your view name.

step 5
Enable your module

step 6
Empty cache (use Devel of Admin_menu module)

Thanks for your great post Mark Jarrell!
Hope this is of any help to others.

I have two page views with exposed filters that I would like to add reset buttons to.

I created a my_form_module.info and a my_form_module.module. I copied and pasted your snippet into the module file. The only change I made to the snippet was to add my two views names as follows:

$exposed_views = array('today2', 'tomorrow');

I enabled my module and refreshed my views page but, alas, no reset button....no errors...no change. I tried emptying cache but that made no difference.

What am I missing? Thanks!

ps I'm using Drupal 6.10 and Views 6.x-2.3

Hello,
thank you for sharing this very much needed function.
Unfortunately, there is an error in the line starting with '#value'. Seems there is something missing in the code?