I want to use two 8-bit PISO shift registers together to make 16 bits. Do I just connect the serial-out pin of one to the serial-in pin of the other? Here is the datasheet: http://www.nxp.com/documents/data_sheet/74HC_HCT166_CNV.pdf

You do realize that is a Parallel/Serial in with Serial output right. Unless you are trying to build a parallel to serial converter or have a specific need to create a serial stream of data you may have the wrong chip. That chip would take in 8 bits in parallel, a clock line, and an enable line. It would then convert that to a stream of bits based on your parallel data at the clock rate.

More commonly people use Serial in , Serial/Parallel out shift registers like the 74HCT595. These take in a serial stream and create a parallel (8 bit output) from that. They can be tied together to create large amounts of control from a few lines of the micro. See my post in the Photography Club Rating Thread where I describe the use of four of the 595's with a 4 digit 7 segment display. I also have sample code there.

Rick