Plain JavaScript:
var e = document.getElementById("elementId");
var value = e.options[e.selectedIndex].value;
var text = e.options[e.selectedIndex].text;
jQuery:
$("#elementId :selected").text(); // The text content of the selected option
$("#elementId").val(); // The value of the selected option
AngularJS: (http://jsfiddle.net/qk5wwyct):
// HTML
<select ng-model="selectItem" ng-options="item as item.text for item in items">
</select>
<p>Text: {{selectItem.text}}</p>
<p>Value: {{selectItem.value}}</p>
// JavaScript
$scope.items = [{
value: 'item_1_id',
text: 'Item 1'
}, {
value: 'item_2_id',
text: 'Item 2'
}];