At the equator the earth receives the most direct and intense radiation from the sun. This heats the air, which is quite humid, and it rises. It condenses at higher altitudes and rain falls over the tropics. The air, now less humid, begins to sink about the latitudes of 25-30 degrees north and south. This sinking dry air is what causes deserts to form at these latitudes.
Air in the tropics along the equator rises, carrying with it moisture that then falls in the tropics. The dry air then sinks at about 25 degrees north and south forming deserts.
For a list of the 26 major desert areas around the world as well as the countries in which they occur, click on this link.
The major deserts of the world occur around 25 degrees N or S because the Subtropical High Pressure Systems are located there. Air in the Subtropical High Pressure Systems is subsiding and warming. As a result, very little condensation occurs and any liquid water in the atmosphere evaporates. Therefore, clouds and precipitation are rare. Rivers do flow through some deserts, but they get their water from locations outside the desert. Much of the tropical desert region (especially in Africa) has few mountains, so their effect in blocking moist air is minimal.
For a list of the major deserts in then world and the countries in which they occur, click on this link.
Actually, there are no real deserts near the equator. This region is known more as a region of heavy rain and rainforests. Most hot deserts occur about 30 degrees north and 30 degrees south of the equator.
For a clickable list of all the major deserts of the world as well as the names of the countries in which they occur click on this link.
There are about 2 dozen major desert areas in the world. For a list of these deserts and in which countries they occur click on this link.
Cacti occur only in the Americas and the temperature can vary from -20 to -40 degrees F. in parts of the Great Basin and Colorado Plateau Deserts in winter to over +130 degrees F. in the Mojave Desert in summer.
Since the area on the equator receives the most direct sunlight, the humid air heats up and rises. In the upper atmosphere it condenses into clouds and rain falls in the tropics. The now-dry air moves to about 30 degrees north and south and sinks, forming a desert.