I think they were used, for transfering data, like USB and Firewire, but in a different way. Not sure on that. But it could, also be used for modems, keys, mouse, and other peripherals. I remember I used it once, way back, for a game. And the gaming controller, used the serial port.
Serial ports are usually used in workstations, IE next time your at a super store have a look at the back of the cashier's computer, the scanner pluges in the serial port (usually)... Alot of hardware that you do not see every day works with a serial port, for example polygraph (Lie detector) systems can use the serial port, Numerous other scientific instruments use it as well.