Wordpress - How do you change the visual editor's background color?

First, add a CSS file in your theme directory (I'm calling it tiny.css). Then add the following to your theme's functions.php:

// Add custom styles to TinyMCE editor
if ( ! function_exists('tdav_css') ) {
    function tdav_css($wp) {
        $wp .= ',' . get_bloginfo('stylesheet_directory') . '/tiny.css';
        return $wp;
    }
}
add_filter( 'mce_css', 'tdav_css' );

Finally, add this CSS to tiny.css

.mceContentBody.wp-editor {
    background-color:#000000;
}

... replacing #000000 with the HTML color code of what color you'd like it to be.

similar to the answer by GavinR, using the wordpress add_editor_style() function; (as implemented in Twenty Ten and Twenty Eleven)

in functions.php of your theme, add:

add_editor_style();

then create an editor-style.css in your theme folder:

.mceContentBody.wp-editor {     
  background-color: #000;
  color: #fff; 
}