How can I show a different theme for admin users? WP 3.8+

You can use the filter stylesheet:

<?php add_filter( 'stylesheet', 'wpse149620_stylesheet' );

function wpse149620_stylesheet( $stylesheet ) {
    if ( ! is_admin() && current_user_can( 'administrator' ) ) {
        $stylesheet="admin-theme";
    }

    return $stylesheet;
} ?>

However, this must be loaded before the first time the “current theme” is requested, which can only be done (without editing core) by putting this in a Must Use Plugin.

Create a directory called ‘mu-plugins’ in ‘wp-content’ and insert this code into a PHP file. WordPress will pick this up automatically. Make sure there are no spaces, line breaks or output before the PHP code to avoid a fatal error.