If I put a shield on an Arduino, can I use the Arduino for anything else? I did some basic Arduino examples in the recent past, but I have never actually seen a shield for Arduino firsthand.

So I wonder: If I put a shield on an Arduino (for example, the Adafruit Motor Shield), does it "block" the entire Arduino, including all input and output pins?

Is it possible to use a shield, and still connect additional components that would usually connect directly to the Arduino (say, a potentiometer, or anything similar)? Does this depend on the type of Arduino, or on the type of the shield, or is it not possible at all?
Normally, yes, you may plug other components to your setup after you plug your shield, but it depends on the shield exposing the unused Arduino pins through additional female headers. 

Some shields even provide a little protoboard or perfboard to make it convenient for plugging or soldering additional components. Below are some examples:




Arduino shields are normally designed to be stackable, so you can plug one on top of the other. See more on Arduino shields from this WikiPedia article. See below one example of stacked shields, shamefully stolen from this great answer by RedGrittyBrick.


Photo by John Boxall

But note that you need to study carefully what pins each of the shields use to avoid conflicts between the boards. Such conflicts may lead to damages.