Not a problem, you can either convert the file from docx to .doc format or use one of the online services to view the content of that file without requiring Microsoft Office Word 2007.
See Guide: How to Convert Files to a Different Format
The DOCX format is the default file extension in Word 2007. It essentially a bunch of zipped XML documents - you can even rename the extension from .docx to .zip and extract the contents using Winzip like any other zip file.
To convert .docx documents to .doc format, all you have to do is download the free Microsoft Office compatibility Pack here and you'll then be able to open, print edit, and save .docx files in Office 2000, Office XP, or Office 2003 [much like an advanced Word 2007 File Viewer].
If you are on Mac, you can get the Microsoft Office Open XML File Format Converter for Mac here - this converts .docx to rtf (rich text format) files which can be viewed in Office for Mac and other Mac word processors.
Alternatively, you can convert .docx to .doc or extract text from .docx files online using Zamzar's email conversion. Unlike the Microsoft compatibility pack, these docx to doc conversion services do not require copy of Microsoft Office.
It is also possible to open and edit a .docx file in OpenOffice or StarOffice using the free Open XML Translator from SourceForge which converts .docx Word documents to .odf and vice versa.
Related: Microsoft Office 2007 FAQ, Office 2007 Fonts Free
The Word 2007 docx format is currently not supported by GMail Word viewer or Google Docs & Spreadsheets.