Of course, the title of this post is a bit misleading. ND Filters on your lens, of and by themselves, do not affect depth of field. What they do affect if the amount of light coming through your lens, potentially reducing it so much that you may need to use a large aperture in the bright sunny outdoors. Large aperture means shallow depth of field. Et voilà!
But what type and how many ND Filters do you use?
David Hobby over at the Strobist has it all carefully explained.
Read the tutorial at: Strobist.