Organized camping is a common alternative, especially in the mainland lake district, but it’s a popular family option throughout the country. In wilder, more remote areas such as Aisén and Magallanes, it’s possible to camp almost anywhere for free except in the most popular places, such as Parque Nacional Torres del Paine [1]. Note that many Chilean campgrounds charge per site (for up to five or six people) rather than per person, which can make camping less appealing economically for single people or couples, who may stay equally cheaply at pretty good budget accommodations.
Links:
[1] http://www.moon.com/destinations/chile/southern-patagonia/parque-nacional-torres-del-paine