Using a 16 bit ADC chip with arduino
The ADS7805 is old but still a pretty good ADC. I could imagine that you just have a few lying around that you want to use. I would simply wire it to two parallel in / serial out chips like the 74HC589 or CD4021 as used in this example:
http://www.arduino.cc/en/Tutorial/ShiftIn  

Start the conversion as described in Duncan C's answer and then simply clock in all 16 bits. I think you could then probably get away with 4 or 5 control lines.