Sounds like you have a border attached to your default paragraph style. Here's how to get rid of it:
(Note: This answer is long because it contains two sets of instructions: One for Word 2007 and one for previous versions.)
In Word versions prior to Word 2007:
1. Click in an affected paragraph.
2. Click on the Format->Styles and Formatting menu item.
3. In the bottom part of the sidebar that pops up, the style for your paragraph should have a bold box around it.
4. Hover the cursor over the style. A listbox arrow should appear. Click it.
5. Select Modify from the list box.
6. Click the Format button and select Border.
7. Under Setting, click the None preview.
8. OK out of everything.
All paragraphs in the document with that style should adjust themselves.
Now, if you want to carry this one step further and fix the style on the template your document is based on (probably Normal.dot, but not necessarily), do this:
1. Click the Tools->Organizer menu item.
2. In the left-hand list box, find and click on the style you changed.
3. Click the Copy button between the two list boxes.
4. Click OK.
When you close your document, you may see a warning message asking if you want to save the changes to Normal.dot. This is an anti-virus measure, intended to alert you that something has changed in Normal.dot. In this case, you made the change, so you want to accept it.
In Word 2007:
1. Click in an affected paragraph.
2. Click the Home tab on the Ribbon.
3. Click the arrow in the lower right corner of the Styles section.
4. The style for your paragraph should have a bold box around it.
5. Hover the cursor over the style. A listbox arrow should appear. Click it.
6. Select Modify from the list box.
7. Click the Format button and select Border.
8. Under Setting, click None..
9. Click OK.
10. If you want this to carry forward to other documents based on the template this one is based on, click the radio button for New Documents Based On This Template.
11. OK out of everything.
All paragraphs in the document with that style should adjust themselves.
When you close your document, you may see a warning message asking if you want to save the changes to Normal.dotx. This is an anti-virus measure, intended to alert you that something has changed in Normal.dotx. In this case, you made the change, so you want to accept it.
That should do it.