The Black Rock Desert Volcanic Field in Millard County, Utah.
Utah has two potentially active volcanoes
The southwestern USA has quite a few volcanoes that could potentially erupt again. They exist in the California upper and lower deserts, Arizona, New Mexico, Colorado, Nevada, and also Utah.
There is also the Yellowstone Supervolcano in Wyoming, and some other volcanoes in Idaho, the mountains of California, and also in Oregon and Washington. The large stratovolcanoes in the Cascades such as Mount St. Helens and Mount Rainier are well known, although many smaller volcanoes in the USA are not so well known.
Active volcanoes are typically defined as having erupted within the past 10,000 years and likely to erupt again someday. By this definition, there are two active volcanoes in the state of Utah.
Vulcan's Throne is a cinder cone near the edge of the north rim of the Grand Canyon in Arizona, and part of the Uinkaret Volcanic Field.  Uinkaret and two of the volcanic fields located in Utah are active and expected to erupt again eventually, although no one knows when it will happen. 
A belt of volcanic fields in Arizona and Utah
Starting at the edge of the Grand Canyon’s north rim in northwestern Arizona, there is a chain of volcanic fields that extend northward into Utah. Some of these volcanoes can be considered active, and others have not erupted recently and are dormant or extinct.
At the edge of the Grand Canyon is the Uinkaret Volcanic Field, which has in the past spilled lava over the edge of the Grand Canyon and blocked the Colorado River. In some places this can clearly be seen. This field is still active.
Further north in Utah are two more volcanoes within this belt that are also considered active, discussed below.
Black lava flow within the Black Rock Desert Volcanic Field. This lava flow is located to the west of Fillmore, Utah and is over six miles (10 km) across.
Black Rock Desert Volcanic Field
Located between the towns of Cove Fort and Delta in west-central Utah, this is the northernmost volcanic field in the belt of volcanoes that extends northward from the north rim of the Grand Canyon in Arizona. It covers about 2,700 square miles (7,000 square km) and is 90 miles (145 km) long.
There have been many eruptions over the past few million years from this location, and the most recent occurred only about 720 years ago, in about 1300 AD, forming basaltic cinder cones and lava flows at a location called Ice Springs near the center of the volcanic field. This eruption occurred about 200 years before the Americas were discovered by Christopher Columbus.
At this location there are many volcano types and features. There are cinder cones, shield volcanoes, lava domes, maars (explosion craters), a caldera, and some lava tubes. The area also has some amazing ancient petroglyphs and geological evidence of the shoreline of ancient Lake Bonneville, which was far larger than Utah’s Great Salt Lake and existed during the Pleistocene until about 12,000 years ago.
The ancient lake covered up evidence of many older eruptions and cinder cones. The disappearance of this lake occurred when a natural dam overflowed, and the water flowed through Idaho’s Snake River Plain and eventually to the Pacific Ocean. The volcanic activity younger than the time that this massive lake met its demise therefore is what stands out best.
The Markagunt Plateau Volcanic Field in southern Utah, to the east of Cedar City and southwest of Panguitch.
Markagunt Plateau Volcanic Field
The exact age of the most recent eruption from this location is not certain, although it is certainly within the past 10,000 years.
Located in Southwestern Utah east of Cedar City, there are dozens of cinder cones at this location. As with most cinder cones, they are monogenetic – meaning they erupted once and then were done and became extinct. More could form in the future however, although geologists have said that the chances are low, and lower than the Black Rock Desert Volcanic Field discussed above.
Overall the Markagunt Plateau Volcanic Field covers about 1,160 square miles (3,000 square km). The oldest eruptions took place over 5 million years ago near what is now the town of Panguitch. The most recent eruptions occurred near the center, southwest of Panguitch, and both north and south of where Panguitch Lake is now located.