If you are using a responsive theme it is essential that you make sure that the navigation works correctly on all devices - it should be clear how it works and shouldnt be too fiddly to use on touch screen devices. Most responsive themes will take into account the navigation and will switch it depending on the screen size of the viewing device but not all themes carry this out correctly which is where you could use an external menu plugin to handle it.

Personally I like to switch the default menu for a drop down select box, you can view this in action on WPLift if you resize the window down or visit on a mobile. I like how the iPhone handles select boxes so this is the method I use in my themes.

If you have more complex menu requirements such as multiple levels or wish to use graphics / icons in the menu then a plugin would be a better way to handle this and there are some great plugins I have found to handle this ...

Free Menu Plugins

Responsive Menu

This is a Highly Customisable Responsive Menu Plugin, with 45 customizable options

Details & Download | Price: Free

WP Responsive Menu

Using WP Responsive Menu plugin you can easily get highly customizable mobile menu plugin for your wordpress site. This plugin can easily convert your wordpress 3.0+ menu to a great looking sliding menu for mobile devices.

Details & Download | Price: Free

Simple Responsive Menu

Make your site simple menu to responsive menu. This plugin is convert WordPress menu to simple responsive menu.

Details & Download | Price: Free

Royal Responsive Menu

The Royal Responsive Menu plugin automatically turns any WordPress 3 Menu into a select box / dropdown on mobile devices.

Details & Download | Price: Free

jQuery Responsive Select Menu

Automatically turns your standard WordPress navigation menus into responsive select / drop-down menus when the screen is below a certain width.

Details & Download | Price: Free

Premium Menu Plugins

MOBILE.NAV - Responsive menu plugin

The easy to use mobile and responsive navigation menu plugin for Wordpress

Details & Download | Price: $10

Revolution Responsive Menu

Turn you existing menu into amazing fly-out responsive menu with a click. Simpy works on any WordPress version or theme.

Details & Download | Price: $11

Mean Menu

MeanMenu is a responsive menu plugin for WordPress which will help you automatically make your menu mobile friendly.

Details & Download | Price: $12

Kodda

Kodda is a responsive , modern , clean & highly customizable WP menu. You can style almost everything from the settings page.

Details & Download | Price: $13

Mega Main Menu

Awesome responsive menu plugin. Features: icons, sticky, mega dropdowns variations, custom skins, fully customizable. You can place any content in dropdowns: links, text, images, widgets and shortcodes. Custom dropdowns so easy with “Mega Main Menu”.

Details & Download | Price: $14

DH Menu

This is user-friendly, highly customizable, responsive mega menu WordPress plugin. It works independently of the Wordpress system menu. With this plugin, your site has a beautiful mega menu , user friendly, responsive or create sliding your menu in mobile apps.

Details & Download | Price: $12

WordPress Menufication

Navigation is one of the most important aspects of a website. The fly-out menu (with inspiration from Facebook) has been proven to be the most efficient navigation that dramatically can improve your visitors experience on your website.

Details & Download | Price: $15

Touchy

Touchy, a mobile-first menu plugin for WordPress. While fast, reactive and primarily meant for touch devices, Touchy can also be used on a full-blown desktop site as it’s been tested in a variety of browsers to ensure it works the same everywhere.

Details & Download | Price: $10

Stimmy

Stimmy is a premium WordPress plugin that generates a responsive navigation menu using your theme standard menu as source.

Details & Download | Price $10