Question: I know there are devices to measure power (e.g., dynamometers) but I can't think of any example of a device that measures work directly. Is there such a thing?

Answer: 
Several things that we don't normally think about as "work meters" effectively measure work.

For instance, if you marked a spring scale with energies instead of forces, you would have a device that measures work done to it.
Note that to know work, you must measure a flow variable, an effort variable, and a time variable. I know of no measurement device that can capture all three "directly" i.e., in a single measurement. 

But in the electrical realm, a work meter is called a watt-hour meter and there's one sitting on the outside of your house, which furnishes the basis for your monthly power bill.

And in the mechanical realm (specifically, steam power) there is a device called an indicator in which the stroke displacement of a piston in a steam engine is drawn onto the x-axis of a piece of chart paper while the steam pressure above the piston is drawn onto the y-axis. the area under the curve is an analog representation of the work done per stroke.