No browsers currently have the code necessary to render Word Documents, and as far as I know, there are no client-side libraries that currently exist for rendering them either.
However, if you only need to display the Word Document, but don't need to edit it, you can use Google Documents' Viewer via an <iframe> to display a remotely hosted .doc/.docx.
<iframe src="https://docs.google.com/gview?url=http://remote.url.tld/path/to/document.doc&embedded=true"></iframe>
Solution adapted from "How to display a word document using fancybox".
Example:
However, if you'd rather have native support, in most, if not all browsers, I'd recommend resaving the .doc/.docx as a PDF file Those can also be independently rendered using PDF.js by Mozilla.
Edit:
Huge thanks to fatbotdesigns for posting the Microsoft Office 365 viewer in the comments.
<iframe src='https://view.officeapps.live.com/op/embed.aspx?src=http://remote.url.tld/path/to/document.doc' width='1366px' height='623px' frameborder='0'>This is an embedded <a target='_blank' href='http://office.com'>Microsoft Office</a> document, powered by <a target='_blank' href='http://office.com/webapps'>Office Online</a>.</iframe>
One more important caveat to keep in mind, as pointed out by lightswitch05, is that this will upload your document to a third-party server. If this is unacceptable, then this method of display isn't the proper course of action.
Live Examples: