OK, I have just been having a play in Maya 7 to figure out what to do...

So here goes:

Create your ribbon (I used a ploy plane)
Create a spiral curve (I used EP CV Curve tool)
Select your Ribbon and the Curve
Go to the Animation Menu Set
Choose Animate > Motion Paths > Attach to Motion Path (Option Box)
Click Edit and Reset
Ensure Follow option is ticked and click Attach
Set the time slider to 150 (ish) and run the animation

Now to create the effect that its soft and following correctly and not stiff...

Select the Ribbon
Go to Animate > Motion Paths > Flow Path Object (Option Box)
Click Edit and then reset
Then click Flow

Run the animation again and its follows, but its still not really accurate.

So in the Channel Box select ffd1LatticeShape and change the S Divisions to about 30. This would be ample enough for a simple curve, but the more complex the curve I would recommend upping the S Divisions to around 60.

Hope this get you on the right path (no pun intended).

Enjoy... I have attached the MA file (Maya 7) for you to refer too