How can I check email exists via a jquery keyup()?

I would use an AJAX request to a PHP script that does the lookup, which might look something like this on the jQuery side after document ready:

// jquery
$('#email-input').live('change', function() {
    //ajax request
    $.ajax({
        url: "email_check.php",
        data: {
            'email' : $('#email-input').val()
        },
        dataType: 'json',
        success: function(data) {
            if(data.result) {
                alert('Email exists!');
            }
            else {
                alert('Email doesnt!');
            }
        },
        error: function(data){
            //error
        }
    });
});

With the example above your PHP would have to return json data once its done the email check based on the address, for example your email_check.php would contain:

// get email passed via AJAX
$email = $_GET['email'];

// do check
if ( email_exists($email) ) {
    $response->result = true;
}
else {
    $response->result = false;
}

// echo json
echo json_encode($response);

Hope that helps!