Solución
$(function(){
$(window).keydown(function(e){
if(e.which === 40){ //down
if($('li.selected').length === 0){ //Si no esta seleccionado nada
$('li:first').addClass('selected');
}
}else if(e.which === 38){ //arriba
$('li.selected').removeClass('selected');
}else if(e.which === 39){ //abajo
var liSelected = $('li.selected');
if(liSelected.length === 1 && liSelected.next().length === 1){
liSelected.removeClass('selected').next().addClass ('selected');
}
}else if(e.which === 37){ //izquierda
var liSelected = $('li.selected');
if(liSelected.length === 1 && liSelected.prev().length === 1){
liSelected.removeClass('selected').prev().addClass ('selected');
}
}
});
});
<ul>
<li>Item 1</li>
<li>Item 2</li>
<li>Item 3</li>
<li>Item 4</li>
</ul>