Yes, but it's a bit tricky. You have to create an "Opacity Mask". Let's say you have a solid blue rectangle that you want to fade.
1: Duplicate the object directly on top of itself. There are several ways to do this; out of habit, I usually just double-click the scale tool, make sure it's set to 100% and click copy.
2: Change the top object fill to a black to white gradient.
3: Select BOTH objects, then open the Transparency palette (Window > Transparency).
4: In the fly-out menu, select "Make Opacity Mask".
That should do it. If you want to alter the gradient, select the object, and both the solid color shape and the gradient mask should be visible in the transparency palette. Clicking on the mask lets you edit it in isolation, so you can use the gradient tool to alter the gradient any way you like. You can also add to it, or change the shape if you like. To stop editing the mask, and return to the illustration, you must click on the left hand thumbnail in the Transparency palette.