I've pieced borders. On one I did recently I had to cut the borders crosswise to get the design in the right orientation. To make the piecing less noticable I carefully matched the design. You can see the seam in the closeup of the border pic but it blends in pretty well on the overall photo.
http://www.quiltingboard.com/posts/list/12200.page
I prefer to put the seam a little off center, especially if I'm piecing both sides. That way I don't have two seams directly across from one another. Hope this makes sense.