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.
I'm having trouble thinking of many things that measure "directly" in general.

The best examples I can think of would be length measurements; but even that is a convoluted physical process involving the comparison of light reflections that humans just happen to be really good at.

I'd say a dynamometer isn't very direct either. They usually measure torque and RPM, or some other variables that can be converted to work.

Basically, measurement is giving mathematical value to something physical. It's hard (impossible?) to make any measurement without a medium.