If on quitting Word, you get a 'save changes to Normal' question, answer yes. Word will ask you to confirm that you want to change the setting for new documents-answer yes. Be sure the 'do not check spelling or grammar' box is NOT checked.
Word will automatically add that language tag to your Normal style, which is the default style for text in a new blank document. Go to Tools>Language, select a Language, and click Default. New documents will behave, although you will need to fix old documents one-by-one. Then anytime you use that style in the future, it will automatically have the language tags. You need to modify the style that the text is formatted in, to include the language formatting. Fixing All Documents, or Changing the Default Language Spelling depends on the language setting, so first make sure you have a Tools>Language menu entry. Note: the Word 2004 Help topic 'Troubleshoot spelling and grammar checking' also addresses some questions not covered here.
Updated for Word 2008 (DRAFT in Progress) Spell-Checking, Language, and Dictionary Issues in MacWord