<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
Why specify a doctype? Because it defines which version of (X)HTML your document is actually using, and this is a critical piece of information needed by browsers or other tools processing the document.
For example, specifying the doctype of your document allows you to use tools such as the Markup Validator to check the syntax of your (X)HTML (and hence discovers errors that may affect the way your page is rendered by various browsers). Such tools won't be able to work if they do not know what kind of document you are using.
But the most important thing is that with most families of browsers, a doctype declaration will make a lot of guessing unnecessary, and will thus trigger a "standard" parsing mode, where the understanding (and, as a result, the display) of the document is not only faster, it is also consistent and free of any bad surprise that documents without doctype will create.