Valles Caldera in Northern New Mexico, as seen from space. The caldera is about 14 miles east to west, and a magma chamber is known to sit underneath the southwest portion. In the photo, the town of Los Alamos can be seen on the right-hand side, just a few miles away from this massive volcano. No eruptions have occurred in 40,000 years, although scientists expect more to occur. When and how large are unknown. 
Three New Mexico volcanoes could potentially erupt again
The definition of an active volcano that is most commonly used by geologists is one that has erupted in the past 10,000 years and is thought to have potential for more eruptions. By this definition, New Mexico has two active volcanoes.
Another volcano in New Mexico has not erupted for longer, not since 40,000 years ago, but may also erupt again. It is currently in a state of dormancy. This volcano had two eruptions, both over one million years ago, that were amongst the largest eruptions to have ever occurred.
After discussing the two volcanoes that meet the criteria for being called active volcanoes, I will discuss the sleeping giant and what scientists know about it.
This article uses some volcanology terms such as caldera, cinder cone, lava flow, and more. For definitions and explanations see my article, Types of Volcanoes and Volcanology Terms.
Carrizozo Malpais is a 50-mile (80 km) lava flow in south-central New Mexico, seen clearly from space in this photo taken by NASA. This lava flow formed approximately 5,000 years ago, over the course of two or three decades. 
A very prominent black lava flow, clearly seen in space photos of New Mexico, is located in the south-central part of the state and is 50 miles (80 km) in length. The eruption is thought to have occurred about 5,000 years ago and went on for two or three decades.
The vent from whence the lava flowed is called Black Peak, at the northern end of the flow. Today it is an 88-foot (27 meter) tall cinder cone rising above the lava flow.
This very long lava flow is one of the longest known to have occurred on Earth in the past 10,000 years. Much of the flow occurred within insulated lava tubes, allowing it to reach such a great length.
The name “Carrizozo Malpais” is in Spanish, and translated roughly to “bad footing,” named for the difficulty of traveling across the lava flow terrain.
The lava flowed from an area of known crustal weakness, called the Capitan lineament, and future eruptions are possible according to USGS. 
In the center of this photo is Bandera Crater, a prominent feature within the Zuni-Bandera Volcanic Field in New Mexico. This cinder cone is about 500 feet (150 meters) tall. 
Zuni-Bandera Volcanic Field
Covering about 950 square miles (2,460 square km) in west-central New Mexico, this volcanic field has a 1.5 million year history in which at least 100 separate vents have erupted. Most of these are cinder cones.
The youngest eruption known from this location occurred about 3,000 years ago. A 26-foot (8-meter) cinder cone spilled lava mostly northward for about 25 miles (40 km) before turning eastward to flow another 6 miles (10 km) down the Rio San Jose Valley.
The second-youngest flows are from Bandera Crater about 10,000 years ago. This cinder cone is 500 ft (150 meters) tall and about 3,300 ft (1 km) wide, and the lava flow to the south extends about 19 miles (30 km).
Cerro la jara is a small lava dome that is covered with forest, and located within the southeastern part of Valles Caldera. The lava dome is about 250 feet (75 meters) tall. To the west and also within Valles Caldera is a much larger lava dome called Redondo Peak, which reaches 11,253-foot (3,430 meters) in elevation. The entire caldera is at high elevation, with the enitre interior being near or above 8,500 feet (2,590 meters). 
Listed on many websites as a “supervolcano,” two massive eruptions that occurred here 1.15 and 1.47 million years ago don’t quite meet supervolcanic standards, although since these eruptions occurred, only six others have occurred worldwide that were the same approximate size or larger. The last time an eruption as large or larger occurred was an eruption of New Zealand's Taupo Supervolcano 26,500 years ago.
Valles Caldera last erupted 40,000 years ago, and thus does not meet the criteria for being considered an “active” volcano. It is dormant but is closely watched and expected to eventually erupt again. Whether an event as large as what happened in the past can happen again is unknown but thought to be unlikely.
Located in the northern part of the state about 45 miles (72 km) north of Albuquerque, and just a few miles from Los Alamos, the caldera is about 14 by 11 miles (23 by 18 km) in size. It is older than two other large calderas in the USA which have potential to erupt again, which are the Yellowstone Supervolcano in Wyoming and Long Valley Caldera in California.
Even many of the most recent eruptions were large enough to have covered most of what is now New Mexico in ash. At present it is known that a magma chamber resides underneath the southwestern portion of the caldera, which is where the most recent eruptive activity originated from.
Eruptions appear to have occurred on average about every 50,000 years in the past, although the spacing between them has been very irregular. This contributes to scientists finding it nearly impossible to predict what this volcano will do in the future.