How to get Word to do line break on Enter rather than paragraph break?

Just modify your style. The default paragraph style in Word 2010 comes with a spacing of 12 pt after the paragraph. If you don't want that, set the spacing after to 0 pt. You can also check the checkbox titled "Don't add space between paragraphs of the same style" to suppress this behavior in your normal paragraphs.

You can find these settings by right-clicking your "Normal" style in the "Home" tab of the ribbon bar -> Modify... -> Format -> Paragraph.