In cartoons, etc., acid is generally shown as vividly green, as in this scene from the Simpsons:
We even have the colour "acid green".
But when I used to use acids in chemistry class, they weren't bright poisonous green. They were mostly colourless, as, for example, this picture of sulfuric acid from Wikipedia:
So where does this idea of green acid come from? Are there acids which are actually green? Or perhaps acids are green when highly concentrated?
The green is the color of bile which usually accompanies gastric acid. Acid in its original context referred to a bitter taste. Bitter tasting compounds, such as vinegar, is what led to the modern chemical definition. The chemical definition is less likely to have influenced the populace than the experience associated the somewhat bitter, acidic, taste of gastric acid accompanied by bile.
Actually, I'd rather say the green-yellowish color is attributed to both toxic chemicals and radioactive waste in general and not only to the super acids. It might as well be that the corrosive acidic stuff seen in cartoons, movies and video games is green due to the cliché introduced by the comic book authors, namely during the Golden Age inbetween late 1930s and early 1950s. The first issue of Batman from 1940 introducing Joker already contains a pool of green waste (BTW it's acidic as we shall see later):
I cannot speak for the exact motives of the comic books' artists, but at that time period there already were several chemicals that could affect the choice of the "acid-green" color for the years to come; I tried to sort them from the most fictional to the most plausible and fitting the "green acid" term:
Copper-doped zinc sulfide ($\ce{ZnS:Cu^2+}$). Polycrystalline samples are capable of green luminescence. Mentioned by Batman as the chemical responsible for the green color of the acid pool in Batman Vol 2, 14, 2013:
Batman: I know its components by heart. The whole list.
Eleven percent sodium hydroxide. Thirty-four percent sulfuric acid. Five percent chromium solution. Zinc sulfide, doped with copper, which gives it its green glow.
I'm purposely leaving no comments on co-existing of $\ce{NaOH}$ and $\ce{H2SO4}$ in the solution, as well as absence of hydrolysis of $\ce{ZnS}$. Bruce Wayne is rich enough to know better.
Fluorescein. The most famous dye tracer known for over hundred years. Fluorescein was used in 1877 to prove that the Danube and Rhine rivers are connected by underground channels. These days is also used for entertainment purposes, e.g. to turn rivers green on St. Patrick's Day. Fluorescein is not acidic (it fact, requires mildly basic medium) and not corrosive or particularly hazardous, but the result of dissolving of the few grams of powder in a ton of water turning it green looks impressive, which could've served as inspiration for artist of that time period.
Scheele's Green $\ce{CuHAsO3}$. Used as a green pigment in XIX century. An acidic copper arsenite salt is both toxic and carcinogenic.
Absinthe. A highly alcoholic green beverage due to the presence of chlorophyll. Not really acidic, but, when consumed excessively, a violent hangover takes place along with xanthopsia (a vision of the surrounding reality in a yellow-green color), not to mention uncontrollable rage, nausea and psychological disorders. Favored by certain painters, probably some comic book artists were also influenced by the aftermath this drink causes.
Used chromic acid $\ce{H2SO4 / CrO3}$. Chromic acid a mixture of concentrated sulfuric acid and potassium dichromate commonly used for cleaning heavily polluted glassware a few decades ago. Initial color is brown-yellowish and is attributed to the formation of chromium trioxide $\ce{CrO3}$. Very strong oxidizing agent and a corrosive substance. As the result of oxidizing organic pollutants, chromium(VI) is reduced to chromium(III) having green color, so that the used chromic mixture gradually changes its color to green, although remaining acidic (and carcinogenic, too). These days is replaced by piranha solution which contains hydrogen peroxide instead of chromium as a more environment-friendly oxidizer.
Chlorine trifluoride $\ce{ClF3}$. A famous "N-Stoff", synthesized on industrial scale in the Nazi Germany from 1938 till 1945. Pale-green liquid below 12 °C or when pressurized. Corrosive on its own, and violently hydrolyses to hydrofluoric $\ce{HF}$ and hydrochloric $\ce{HCl}$ acids. Has been proposed as a rocket propellant, poison gas, incendiary and corrosive agent to penetrate metal alloys and concrete. Probably comes as close as it gets to the definition of the "green acid of choice for a super-villain".
Finally, it's also worth noticing that the green-yellowish color of approx. 550 nm $\color{#80FF00}{\Large\bullet}$ is the most noticeable color to the human eye under usual ambient daylight conditions, helping to quickly adjust viewer's focus to what's more important or to just overwhelm.
One chemistry related answer could be that chlorine gas has a greenish hue after which it was named(wikipedia):
Sir Humphry Davy in 1810, who named it from Ancient Greek: χλωρóς (khlôros) "pale green
Also, chlorine gas is closely related to hydrochloric and hypochlorous acid:
Solutions of chlorine in water contain chlorine (Cl2), hydrochloric acid (which is arguably the most commonly known acid), and hypochlorous acid:
$\ce{Cl2 + H2O <=> HCl + HClO}$
Finally, in WWI, chlorine gas was used as a chemical weapon, that caused acid burns to skin, eyes and lung:
By April, German chemists had tested a method of releasing chlorine gas from pressurised cylinders and thousands of French Algerian troops were smothered in a ghostly green cloud of chlorine at the second Battle of Ypres. With no protection, many died from the agonies of suffocation
