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: 
An old method to measure mechanical work is the [Prony brake](https://en.wikipedia.org/wiki/Prony_brake). One measures with a spring balance the torque $T\_p$ exerted by an immovable lever with an adjustable brake on a rotating axis (e.g. of a motor) and then counts the number of turns of the axis. The torque already has the dimension of work. The work performed by $n$ turns of the axis is given by $$W=2\pi n T\_p$$ In this method, the mechanical work is transformed into heat generated by the friction of the brake.
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.