Many Word users find visible spaces useful, since it lets you know when
there are extras... it's a helpful diagnostic. It's especially useful to be
able to instantly seen whether something is a space versus a tab.
However, if you want to hide them... in Word 2003, Tools - Options - View,
remove the check next to Spaces under Formatting marks. Anything not checked
in that section will now toggle on/off when you click the Show/Hide tool.
In Word 2007, those settings are found in Office button - Word Options -
Display tab.