I see this often, as I copy and paste from websites and all sorts of stuff. Word is attempting to bring over the format of the copied area. What you are seeing is the result.
If you are trying to copy and paste text and only want the text, try opening notepad and pasting there first. The text will lose its properties from the copied page. When you paste to Word, the only format that should be placed on it is the font/color/size property. At that point, you can format the text however you want.
Edit: You shouldn't have to save the document, but in some cases it helps to cement the removal of the format from the location where you copied the text.