Eraser tool Settings
The Eraser tool actually works like a Brush. If you double click the tool in the Toolbox you can set the Brush diameter, angle and roundness, and if you have a pressure sensitive tablet you can take advantage of that too. I don't use one, but if you do a lot of illustration work I bet this is a cool addition.
What can and can't
One way to use the Eraser tool is by simply cutting a whole in one or more selected objects. The Eraser tool works upon selection. The Eraser will not work on images, text, symbols, graphs, and gradient meshes. To Erase text you'll need to create outlines first (Text > Create Outlines or Cmd/Ctrl + Shift + O). For symbols or graphs you'll need to expand them (Object > Expand).
When you hold down the shift key, you can erase straight lines. What I particularly like about this technique is that Illustrator automatically closes the paths for you.
Although I don't use the 3D effects very often, it seems the effect will remain after creating a whole in it. In the example below I'm using the Revolve effect on some text that I have created into outlines first.
To erase parts of a stroke with a custom brush applied, you'll first need to expand its appearance (Object > Expand Appearance…).
Each segment of the path will have the brush reapplied. So by expanding its appearance, you turn the stroke into fill and things will be erased as expected.
Another example is when you use the new (CS5) stroke Width tool. You'll also need to expand the appearance first or you'll get weird results.
Smart way to erase areas
The way I use the Eraser tool mostly these days is whenever I have to erase a whole area. It often happens that certain parts of paths grow outside my composition area. In a lot of cases I will opt for a Layer Mask to hide these parts, as this is a flexible nondestructive solution, but a fast and easy option is simply to use the Eraser tool, and hold down both the Shift and Alt/Option keys while dragging over the area that you want to remove (see image below). It will be remove in now time, and Illustrator will close all my paths for me. You gotta love that. Simple, fast and clean.