Ho sistemato un po il codice e ho cambiato alcuni id dovrebbe andare (da verificare se usando il tasto submit il form venga eseguito ugualmente in tal caso cambialo con un button)
codice:
<!DOCTYPE html>
<html>
<head>
<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
<title>testLogin</title>
</head>
<link href="css/login.css" rel="stylesheet" type="text/css" />
<script src="jq/jquery-1.11.1.js"></script>
<body>
<form id="login" method="post" action="">
    <fieldset id="inputs">
            <input id="user_name" name="user_name" type="text" placeholder="Username" autofocus required> 
            <input id="pass_word" name="pass_word" type="password" placeholder="Password" required>
        </fieldset>
        <fieldset id="actions">
            <input type="submit" id="sub_mit"  value="Collegati" name="log">
            <br />
            <br />
            <br />
             <label id="mex" style="display: none;">ffff</label>
            <!--<input id="cc" name="cc" type="text">-->
        </fieldset>
    

</form>
</body>
<script>
$(document).ready(function(){
    $('#sub_mit').click(function(){  
          $.ajax({             
            url:"Login.php",           
            type: "POST", 
            data: {'username': $('#user_name').val(), 'password': $('#pass_word').val()}, 
            //data: { username: "nico", password: "1"}, 
            success:function(result){ 
                //alert(result)
                 if (result=='err') {
                    alert('errore')
                 }
                 else
                 {
                    alert('ok')
                 }
            } //fine success
        
    
        }); // fine .ajax
    }); // fine .click
    
}); //fine document ready
 
</script>
 
</html>