Wordpress - How do I remove UL on wp_nav_menu?

Actually, WordPress supports this by default:

wp_nav_menu(array(
    'items_wrap' => '%3$s'
));

The default for items_wrap is <ul id=\"%1$s\" class=\"%2$s\">%3$s</ul>.

The function wp_nav_menu takes an argument of fallback_cb which is the name of the function to run if the menu doesn't exist. so change you code to something like this:

function wp_nav_menu_no_ul()
{
    $options = array(
        'echo' => false,
        'container' => false,
        'theme_location' => 'primary',
        'fallback_cb'=> 'fall_back_menu'
    );

    $menu = wp_nav_menu($options);
    echo preg_replace(array(
        '#^<ul[^>]*>#',
        '#</ul>$#'
    ), '', $menu);

}

function fall_back_menu(){
    return;
}

you can even remove the container from the menu and do other stuff with some more arguments sent to the wp_nav_menu function

Hope this helps.

The below code should simple do it.

<?php 

  $my_menu = array( 
  'menu' => 'main-menu',
  'container' => '',
  'items_wrap' => '%3$s' 
  );

  wp_nav_menu( $my_menu );

?>

Reference this link for the wp_nav_menu function http://codex.wordpress.org/Function_Reference/wp_nav_menu