International System of Units

i'll call it the metric system, it is abbreviated as SI (from the French Système International d'Unités). If we had to pick a single system, this would be our best bet. What it lacks in whimsy, it makes up for in coherence.

English Units of Measurement

England's measurement system, abandonware since 1826, but the mother system of Imperial and USCS

Imperial

the post-1824 measures used in the British Empire and countries in the British sphere of influence

United States Customary System

freedom units, I'll call them USCS.

cgs

centimeters, grams, seconds, often used in the medical sciences

mks

meters, kilograms, seconds, basically engineering units of the metric system

fps

foot, pound, second, used in the U.S., Liberia, and Myanmar

English Engineering Units

USCS, but with extra steps. lbm or slugs for mass, lbf for force

Farming Units

Bushels, pecks, dry pints

Honorable Mentions / Absurdities

Anthropic Units

Hands, feet, cubits, pace, span, inch, fathom