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.
If you've ever lifted an object on a pulley, the height of the object functions as a 'work meter'. 

Another way to measure work is to convert the energy to heat and measure a temperature rise, which is the principle behind calorimeters. 

A third method is to indirectly use chemistry. You can calculate the total energy released by a battery given the energy released in each individual reaction. Similarly, you can loosely estimate how much work a human is doing by seeing how much $\text{CO}\_2$ they exhale.