No, but the far-sighted would be wise to do so. Closing the elements makes working with style sheets much easier. Closed elements also make the document easier to debug. XHTML makes it a requirement for every element to be closed, so any <li> tag should end with </li> tag, any <p> should end with </p>.

In fact, XHTML goes so far as to require elements be closed even if they don't normally have an end tag. So, any <br> becomes either <br /> (note the space before the /) or <br></br>. Same with <img>, <hr>, <input>, <meta>, and other similar tags. Doing this now will not cause problems with older browsers.