Well, the only wheel I know that works with PS2, Xbox, and Gamecube is the Mad Catz Universal. It's a simple wheel with two way stick shifter, paddle shifters, buttons on the front, and pedels.
I have one of these I bought for my Dreamcast (different model), and it works well with Test Drive 6 and a few other racing games. And you can calibrate the wheel, so it works better with whatever game you choose, though unfortunately this must be done EVERY time you turn on your system as it has no memory.
It also doesn't have a GREAT feel. Though it used to be $60, it's just not as well put together as some wheels. So I'm not sure how long it would last with continual use, etc. One of the BIG selling points for me on the new Driving Force Pro, was reading a PC user had used it for 3 months +, and it was still as solid as the day he bought it. I certainly couldn't say that about my Thrustmaster Digital 2 or some other wheels I've used.
All that said, for the $30 I've seen it for some places, if you can still find one it's a cheap way to drive on ALL your systems. So maybe that would work for you.