According to About.com, the Earth creates mountains through plate tectonics, where its crust is broken into plates constantly in motion, causing stress and uplifting in order to grow mountains. While growth is slow due to these forces, it does happen.
Volcanoes add to the mass of a mountain over time. Some of the largest mountains in the world are lava domes. Vents in the Earth's crust allow lava to flow outside the crust, building taller mountains. Vents in the ocean floor are responsible for building the mountains, such as those that form the Hawaiian Islands.
LiveScience reports, "The mountains in Europe are growing taller and melting glaciers are partly responsible." Scientists studying these mountains find that with less glacial ice, the elastic earth is pushing the French Alps upward at a rate of 0.035 inch per year. In 50 years, at this rate, they are expected to be 1.8 inches taller.
Weathering is the process of breaking down mountains. About.com quotes the film "Planet of Man: The Uneventful Day" as saying, "Water carries the mountains down to the sea a teaspoon at a time. A day becomes a million days, and a mountain of rock changes shape." This same weathered mountain becomes the material that tectonic plates eventually push back from the ocean to form new mountains in the continuous cycle that affects the planet's crust.