As mentioned in another thread, it highly depends on which chipset the usb to serial adapter is designed with.
There are several companies that makes usb serial adapters, the most commonly used chipsets are:
Prolific is the cheapest but also the worst, the drivers/chipset are simply incompatible with many devices and operating systems, including 64-bit systems. The best chipset/drivers are the FTDI. These are very solid and compatible with most devices and almost all operating systems both 32 and 64-bit. These usb serial adapters are a bit more expensive but well worth the money.