Screened serial cable - Connect screen to ground pin
This depends on the application. The signal ground fills two purposes:


Even out voltage potential differences = fundamental electronics. 
Act as a clean signal reference, as opposed to the "dirty" supply ground.


Some applications are less picky than others, and then you can "cheat" by not using a signal ground, but let the supply ground act as reference. This might work ok if the supply is decent and there are no high currents in the system. But for industrial/automotive applications, a dedicated signal ground is almost certainly needed.

The shield is there for another purpose entirely, namely to protect against immunity/emissions. It should only be connected on one side, to a ground different from the signal ground (for example supply ground, chassis etc). Depending on baudrate, environment etc, a shield may or may not be needed.