If you think Illustrator has the same look and feel as Photoshop, you couldn't be more wrong. Creating those nice shiny orbs in Photoshop is one of the easiest things to do, but in Illustrator it takes a lot more effort to get it right. That's why I decided to write this tutorial. After walking through this tutorial, you'll not only know how to create those nice glass orbs, but you'll also have learned how to create gradients with opacity, which is not a standard feature in Illustrator.
 

Step 1: Create a new document, it doesn't matter what size, because you can resize vector graphics to any size you want without losing quality.

Grab your Ellipse Tool and make a circle in the center of your document. With the circle selected, press the gradient button and create a nice radial gradient. 'What?!' I hear you say. You can find the gradient button underneath the stroke and fill colors, it's the middle one of the three small icons.

You can adjust your gradient in the gradient palette (if you don't see it go to Window > Gradient of press F9). Make a gradient similar to the one I created on the right. It doesn't matter which colors you use, as long as you have the light one on the left and the darker one on the right. Slide the little diamond all the way to the right, this way the darker color will only be visible on the outside of your circle.
 

Step 2: Grab your Ellipse Tool once more and create an ellipse in the top part of your circle and fill it with white. You should now have something similar to the image on the right. Copy this layer by dragging it on the 'Create New Layer' icon on the bottom of the layers palette. This way you make sure your copy stays in the same position as your original. If you just copy the shape it usually ends up in a different position.

Make a gradient from top to bottom with white on top and black on the bottom. In the next step we'll work our magic and create the transparent gradient.

Step 3: Select both ellipses you just created by holding CTRL and clicking on the small small circles in the layers palette. If you did it right there will now be two blue squares in you layers palette.
Now go to your Transparency palette and click on the little arrow on the top right and choose Make Opacity Mask.

If you can't find your transparency palette go to Window > Transparency or press Shift+F9.

NB.  If you are using a Mac, replace the CTRL key with OPT.

Step 4: Step 4??? There is no step 4! You're done! And, if you did it right, you should end up with something that resembles my example on the left.

Of course, you can use this with any shape possible but you will have to be more creative with the highlights. The underlying technique will be the same for all of them.