This might not be the right term, but you the ones...where you type one character and the box 'suggests' all the words you have entered before beginning with that letter. For example, the search boxes on any search engine.
So how do I clear such a box's 'memory'? And can I clear the memory on just one type of box?
I believe the term you are looking for is autocomplete. Assuming that you are using Internet Explorer, you should be able to clear the box by going to Tools -> Options -> Content -> Autocomplete, and then pressing "Clear Forms".
Herman