Solution 1

Listen to mousedown instead of click.

The mousedown and blur events occur one after another when you press the mouse button, but click only occurs when you release it.

Solution 2

You can preventDefault() in mousedown to block the dropdown from stealing focus. The slight advantage is that the value will be selected when the mouse button is released, which is how native select components work. JSFiddle

$('input').on('focus', function() {
    $('ul').show();
}).on('blur', function() {
    $('ul').hide();
});

$('ul').on('mousedown', function(event) {
    event.preventDefault();
}).on('click', 'li', function() {
    $('input').val(this.textContent).blur();
});

http://stackoverflow.com/questions/10652852/jquery-fire-click-before-blur-event