Cotopaxi in Ecudaor is located only slightly more than 20 miles (32 km) from the metro area of Quito, which is Ecuador's capital city. It is the second-highest peak in Ecuador, and the second-highest active volcano on Earth, trailing only Llullaillaco, which is also in the Andes Mountains and sits on the border of Argentina and Chile.
Cotopaxi, Galeras, and Nevado del Ruiz
Judging how dangerous a volcano is requires weighing various factors such as its eruptive history, what volcanologists do and don’t know about what it might do in the future, the volcano’s proximity to populated areas, and the types of eruptions the volcano produces.
Due the partially subjective nature of judging the dangerousness (or lack thereof) of any volcano, many lists appear online and elsewhere, which vary from one another. In other words, it's debatable.
From my own analysis, I’ve decided three volcanoes in South America are the most dangerous on the continent. All are stratovolcanoes located in the Andes Mountains, and in close proximity to populated areas. Two are found in Colombia and one in Ecuador. Other volcanoes in South America are more active, but pose less of a risk to humans.
For those unfamiliar with basic volcano terminology, see Types of Volcanoes and Volcanology Terms.
The second-highest peak in Ecuador, at 19,347 ft (5,897 meters) above sea level, is located just over 20 miles (32 km) from the capital city of Quito and its metro area with a population of over 2.5 million people.
In the past 300 years, Cotopaxi has erupted more than 50 times. The large crater at the top is 800 x 500 meters (2,600 x 1,600 feet) in size, and 250 meters (800 feet) deep. The volcano has glaciers, rare for any mountain located at latitudes close to the equator.
A major eruption has not occurred since 1904. A small eruption occurred in 1940, and then after more than seventy years of silence, the volcano awakened again with another small eruption in August 2015 that has continued into early 2016.
If a massive eruption were to happen, the majority of Quito and its metro area could be heavily damaged. Another sizable town further south, Latacunga, was completely destroyed by Cotopaxi three separate times, in eruptions which occurred in 1744, 1768, and 1877, and there is certainly potential for a repeat.
Galeras issuing steam. This is the most active volcano in Colombia.
Our next Andean stratovolcano is located in the southern portion of Colombia, with the peak 33 miles (53 km) from the border with Ecuador. The mountain reaches to 14,029 ft (4,276 meters), and the city of Pasto sits just a few miles east of the crater, at the foot of the volcano, with a population of approximately half a million people.
This is the most active volcano in Colombia, although eruptions are typically smaller and not a danger to Pasto. The most recent eruption was in 2012. However, massive eruptions have occurred occasionally over tens of thousands of years, and will likely happen again eventually.
Pasto sometimes has ash raining down, and other times residents nearest to the volcano are evacuated as a precaution. 
This is the crater at the summit of Nevado del Ruiz in late November 1985, just days after an eruption destroyed the town of Armero and killed a majority of its inhabitants.
Nevado del Ruiz
The final Andean stratovolcano discussed here is the second-most active volcano in Colombia, after Galeras. Located 280 miles (448 km) northeast of Galeras, several sizable towns are nearby, and 80 miles (128 km) to the east is the capital city Bogotá, with a metro area of over ten million people. The volcano most recently erupted during 2014 and 2015.
The volcano’s peak stands at 17,457 ft (5,321 meters), and like Cotopaxi, it has glaciers. Glaciers on volcanoes mean potential massive mudflows, called lahars, if they melt as a result of volcanic activity.
In 1985 lahars from Nevado del Ruiz buried the town of Armero, killing 25,000 people. Currently, at least half a million people are in potential danger of lahars from this volcano. The Armero tragedy of 1985 is one of the worst volcanic disasters known to have ever occurred.
If just ten percent of the glaciers atop Nevado del Ruiz were to melt, the volume of the resulting lahar would be comparable to what occurred in 1985. A massive eruption would melt the glaciers much more, as the tragedy of 1985 occurred with a relatively small eruption, registering level 3 on the Volcanic Explosivity Index.
Volcanoes in the Andes Mountains
There are over 100 active volcanoes in the Andes Mountains, which is the longest mountain range on land (the mid-ocean ridges are longer). In total, the mountains extend about 4,300 miles (6,880 km), roughly paralleling the western coast of South America. They contain the tallest peaks in both the Western and Southern Hemispheres, and of anywhere outside Central Asia.