DrupalSN posted a nice guide to styling exposed View dropdown menus with a JQuery plugin and some stylish CSS.  The guide there worked perfectly except for the step where he hid the submit button.  I changed this:

.views-exposed-form label,
.jquery_dropdown_page .views-exposed-form .form-submit {
  display: none;
}

to this:

.views-exposed-form label,
.views-exposed-widget .form-submit {
  display: none;
}

Also, I wanted a fancy hover effect over the dropdown menu itself, so I added the following style and created a hover version of the background image for the dropdown menu:

div.jquery_dropdown_header:hover {
  background:url(images/jquery_dropdown-header-hover.png) left top no-repeat;
}

Why the module?  The module turns your select box into an unordered list which is much easier to style.  My only gripe is that it fails to show the "any" option on the exposed dropdown once you navigate away from it (it shows up fine on the initial page load).