If you use Modernizr, it is very easy to use Modernizr.touch as mentioned earlier.
However, I prefer using a combination of Modernizr.touch and user agent testing, just to be safe.
var deviceAgent = navigator.userAgent.toLowerCase();
var isTouchDevice = Modernizr.touch || 
(deviceAgent.match(/(iphone|ipod|ipad)/) ||
deviceAgent.match(/(android)/)  || 
deviceAgent.match(/(iemobile)/) || 
deviceAgent.match(/iphone/i) || 
deviceAgent.match(/ipad/i) || 
deviceAgent.match(/ipod/i) || 
deviceAgent.match(/blackberry/i) || 
deviceAgent.match(/bada/i));
if (isTouchDevice) {
        //Do something touchy
    } else {
        //Can't touch this
    }
If you don't use Modernizr, you can simply replace the Modernizr.touch function above with ('ontouchstart' in document.documentElement)
Also note that testing the user agent iemobile will give you broader range of detected Microsoft mobile devices than Windows Phone.
Also see this SO question