As pretty much everyone else has said use ID for one-off elements and class for multiple use elements.
Here is a quick, over simplified example, take HTML and HEAD tags as read
<body>
<div id="leftCol">
You will only have one left column
</div>
<div id="mainContent">
Only one main content container, but.....
<p class="prettyPara">You might want more than one pretty paragraph</p>
<p>This one is boring and unstyled</p>
<p class="prettyPara">See I told you, you might need another!</p>
</div>
<div id="footer">
Not very HTML5 but you'll likely only have one of these too.
</div>
</body>
Also, as mentioned in other answers ID are well exposed to javascript, classes less so. However modern javascript frameworks like jQuery leverage class for javascript too