See http://www.shaunakelly.com/word/styles/FormatOfTextChanges.html

Instead of just pasting the selection, choose Edit/Paste Special, and then select to paste it as unformatted text.  

Sometimes, the pasted selection will assume the formatting of the destination document's paragraph style with the same name, and sometimes the pasted selection will assume the attributes of the default paragraph style, even though it looks like you're pasting it into a modified paragraph.  So, be sure that the destination paragraph style in the destination document has the formatting you want.  

One always useful trick is to avoid pasting into a blank paragraph, but to add brackets to the destination document's paragraph having the desired attributes; then paste (unformatted) between the brackets.