Just to clarify what is being said here....
As originally stated, the Amiga's 9-pin ports are NOT serial ports. They are Amiga mouse/joystick ports. Completely electronically different from a serial port. Plugging a PS/2->Serial adaptor into one of these ports can be VERY harmful to the device or the Amiga, as the power is on a different pin. (and even if you moved the power to the correct pin, the joystick port still has no way of reading serialized data - it's a totally different port.) The only things you should ever plug into an Amiga mouse/joystick port are Amiga mice, Amiga-specific mouse adapters, or Commodore/Amiga/Atari joysticks.
Now, you CAN use an old serial mouse on an Amiga, but through the 25-pin serial port on the back of the machine. You could use a 25pin serial -> 9pin serial adapter, then use the 9pin Serial -> ps2/serial adapter, and then plug in a dual-mode serial/ps2 switchable mouse. You'll then need to load the custom serial-port mouse drivers for the Amiga, and the mouse will only work in workbench and workbench-friendly applications. It is only an exercise of complete pedantics that this is mentioned, though. While you CAN do this, I have no idea WHY you'd ever WANT to do this... It is MUCH less hassle and MUCH MUCH more compatible to just get an Amiga mouse.
