USB-to-Serial cable based on the Prolific chip - Windows 7 driver problem
Original answer from capcom:
I found a very simple solution which I did not find listed anywhere, which is why I am outlining it here to help anyone else who may run into a similar problem in the future. I am running a Win7 64 bit machine.

Open Device Manager
Navigate to your device (it should have a yellow exclamation mark on it)
Right click on it, and choose update driver.
Click Browse my Computer...
Click Let me pick from a list...
A list of all of the drivers should show. Choose the oldest Prolific driver on the list. I chose version 3.2.0 from 2007
Install it, and you're done!

If you are using PuTTy, note that when you connect, the COM port may not work as expected. What you should do, if you need to, is go into the Serial options in the main PuTTy window, and turn off flow control.
Everything should work right now.