HTML <select> what is the name of on select event?

Is onchange what you're looking for?

It's also worth mentioning that this doesn't fire if the selection doesn't change (seems self explanatory). As far as I know there is no event that fires when a user drops down the selectbox and then reselects the original value.

It's onchange Event.

jQuery wraps it in the .change helper. If using plain Javascript then use addEventListner('change', function...):

<html>
<head>
    <script type="text/javascript" src="jquery-1.2.6.js"></script>
    <script type="text/javascript">

// If using jQuery
$(document).ready( function() {
    $("#list").attr( "selectedIndex", -1 );
    $("#list").change( function() {
        $("#answer").text( $("#list option:selected").val() );
    });
});
    </script>

    <script type="text/javascript">

// Plain Javascript:
document.addEventListener('DOMContentLoaded', function(event) {
    var selectList = document.getElementById("list");
    var divAnswer  = document.getElementById("answer");
    selectList.addEventListener("change", function(changeEvent) {
        divAnswer.textContent = selectList.value;
    });
});
    </script>

</head>
<body>
    <div id="answer">No answer</div>
    <form>
        Answer
        <select id="list">
            <option value="Answer A">A</option>
            <option value="Answer B">B</option>
            <option value="Answer C">C</option>
        </select>
    </form>
</body>
</html>

Regardless of input type, whenever a form input changes value, an onchange event should always be thrown. (With the exception of buttons, as they are not really input devices as such.)