"A large crater caused by the violent explosion of a volcano that collapses into a depression " Source: Wikiwords

Arizona examples: The Inner Basin in the San Francisco Peaks is a caldera. The Superstition Wilderness is formed by several calderas.

Hippiepunkpirate's elaboration: As taught in university geology classes, a caldera results from the collapse of a magma chamber, which forms a depression or crater, typically of steep sides. Calderas can be seen in multiple types of volcanoes, and take on different forms depending on lava/magma types.

The most classic stratovolcano calderas are perhaps in the Cascade Range of the Pacific Northwest. Crater Lake is a beautifully preserved caldera which results from the collapse of the magma chamber of the pre-historic Mount Mazama. The most recent major eruption of Mount Saint Helens in 1980 also resulted in a caldera, but one which shape was quite unexpected. When Saint Helens unleashed its fury, the discharge was concentrated out one side of the volcano instead of a typical upward eruption, which left a U-shaped caldera with one side missing. The caldera of the San Francisco Peaks is of a similar shape, and it is thought that the Peaks may have erupted in the same manner as the 1980 Saint Helens event.

Very popular in today's American pop-culture is the idea of the Yellowstone "super-volcano". Yellowstone is actually an excellent example of a recurrent calderic eruption, in which viscous silica-heavy magma causes a build-up then release of pressure over relatively consistent time periods. Each release of pressure causes the collapse of the magma chamber, forming a caldera, hence the name recurrent calderic eruption. These types of eruptions build up pressure for hundreds of thousands of years, resulting in major violent events that are hundreds and even thousands times more explosive than the 1980 Saint Helens eruption. These intensely big eruptions are why Yellowstone is referred to as a "super-volcano". In order for pressure to build for a long time, the magma chambers below these volcanoes are huge, and the calderas formed are also huge. The Yellowstone caldera itself covers an area 35 by 45 miles. The caldera features formed by such eruptions are often hard to make out due to the large and violent scale of the event, and the possibility of multiple calderas overlapping each other. Such is the case for the Superstition Mountains, an extinct recurrent calderic volcano. Another example of recurrent calderic activity in Arizona is the Kingman area, which had such activity about 35 million years ago. The caldera is highly eroded and faulted, so is hard to make out even to well-trained geologists. However, evidence of the volcano is most easily seen but the presence of the Peach Springs Tuff, a volcanic feature very prominent in the Kingman area. A large road-cut on the right of way for I-40 near Kingman exposes the Peach Springs Tuff beautifully, with numerous fault-lines being discernible by a marker bed with the tuff.

Calderas are also possible in mafic shield volcanoes, such as the Hawaiian Islands. In fact, the summit crater of Hawaii's Mauna Loa, the largest volcano on earth by volume, is formed by a beautiful caldera called Mokuʻāweoweo. I cannot find an example of a caldera forming directly from a cinder cone volcano, but this is not surprising considering the small size of cinder cones, and the fact that they are commonly spawn from the magma chambers of larger volcanic structures. Mauna Loa in fact has cinder cones grown within the confines of its summit caldera.