Here's an image I just finished intended to be letterpressed. If you're not familiar with the letterpress process, visit www.StudioOnFire.com to see some lovely examples. Letterpress printing is very tactile and very beautiful to feel and see.
I don't handle printing much anymore, but when I was a graphic designer years ago, we would regularly select colored paper and print Pantone inks. After we started using Epson printers (with white paper) to mock-up projects for client approval, and 4-color printing became much more economical, our design solutions evolved into ever increasingly 4-color process designs printed on white stock. Today, where full color is everywhere, I think it's interesting that limiting your designs to one or two colors actually allows your work to stand out in the crowd.