Virtually every plant sheds its older leaves at some point as part of its natural life cycle. Young, new, vigorous growth manufactures food for the plant, and when the older leaves are no longer needed, the plant sheds them. But if a plant is distressed by environmental factors (including being too dry, wet, or cold, or not getting enough light), the leaves can fall off earlier than they should, so you'll want to make sure the plant is experiencing the right conditions.
Most succulent plants, such as crown-of-thorns (Euphorbia milii), originate in regions with intense sunshine and prolonged drought and have adapted to their environment by being able to survive for long periods without water. Succulents make good house plants because they thrive in the lower humidity found in most houses.
Succulents need lots of sunlight, so place them in a window with a southern exposure. When natural light levels are low, mimic the dry-season needs of the succulent plant by watering them less frequently. Be sure to grow succulents in a potting medium that drains freely and has lots of grit or perlite. The right potting medium offers another way to make succulents feel at home in your house.