I don't use them. My printer is USB and I don't have any external modems for my serial port. A lot of PC's these days are not being manufactured with the serial ports anymore, because there aren't many devices that require them. In my line of work, I deal with a proprietary cable that requires a serial port connection, and we have a lot of customers who complain because the new pc's these days all have USB ports and no serial ports. There are USB to serial adapters, but a lot of the cheaper ones don't seem to be very stable in transmitting the serial data. As for parallel ports, I believe there are still quite a few parallel port printers out there, so it would make sense if that port stayed around for a while.
When I buy laptops for my Firm now, I have to be very careful to be sure it includes serial and parallel ports. Most do not. However, many people with whom I work still have parallel printers so they need them.
I have one device at home that requires a serial port.
Not only are traditional serial ports being removed, but PS2 type keyboard and mouse ports as well. I use Ghost to image PCs at work. This requires DOS and DOS can't recognize a USB keyboard. So, we have to order a serial port with PS2 keyboard connector for our new Dell Optiplexes because the Optiplex no longer comes with PS2 keyboards.