Just got Office 2008 and wrote my first Word Doc. I noticed that the format saved in was .docx not .doc. Does this have any consequence if I send a note to someone who doesn't have Word 2008, such as Windows people, etc, etc.
Yes, very much so. That is the new format for Office 2007 (Windows version) and Office 2008 (Mac version) that is NOT compatible with older versions of Office.
You will need to save as Office 2003/2004 format if you send the file to someone who does not have Office 2007 for Windows or Office 2008 for Mac.
How odd, that website states that the format isn't supported by OS X. Yet Textedit can open and edit .docx files, and Quicklook can display any office 2007 file.