Inverters turn DC into AC. These are extremely common. What is uncommon is "clean" sine-wave AC power. It's cheaper to build step-wave bridge circuits for high-current purposes. Step waves require a bunch of switching regulators, whereas sine-wave requires splitting your signal into three phases (meaning three times the wiring and circuits).
Rectifiers turn AC into DC. These are probably more common than you might imagine. Your computer's PSU is a rectifier. All those little power dongles for your Ipod, radio, Xbox, and laptop are rectifiers. Again the main problem is "clean" power -- in this case it is the "ripple" inside the "DC" voltage.
In terms of the ease of conversion, they are both equally easy. A sine-wave inverter will cost more than a 1mv ripple rectifier, simply because of the extra circuitry and materials involved.
@Skybird--
It's strange that you would be needing 9v AC for a computer (even if it's a chess computer). I would imagine that you actually just need the right rectifier. If the rectifier is hard-wired into the unit and you're trying to run it from your car, well then, yeah -- I could understand the need for an inverter if it was a 220v output like the rest of Europe's AC. In the States, 12vDC-to-120vAC inverters are cheap to find.
A 75w inverter costs $16, and would certainly power that thing.
Heh. You could probably buy a good 220v to 120v "converter" for $20, and use it like that. Highly inefficient, of course, but it would work.