It's tempting to begin with a plug for my business, which is really just a commercialized manifestation of my interest in open hardware, but I think that in the name of promoting an even and balanced approach to free culture, I will start with something I am not personally involved with.
The Arduino is one of the most versatile little microcontrollers I've seen, and it's entirely open-source! Check out their Hardware page if you're interested in building your own chip from scratch, although that requires some seriously specialized equipment. If you'd rather, you can purchase an already-made board with a good amount of I/O at the main website, or at MakerShed, which you can access through the MakeZine link on the left of the blog.