The US Bureau of Land Management operates a program that allows individuals who qualify to adopt wild horses and burros that live on Federal land.
These animals are descendants of horses and burros that escaped or were released by Spanish explorers, ranchers, miners, members of the US Cavalry and native Americans. Since the program began in 1971, almost a quarter million wild horses and burros have been adopted.
To qualify you must be at least 18, and be able to demonstrate that you can provide for the needs of the animal. You'll need an enclosure at least six feet high, where you can keep the animal until it is gentled - the BLM notes that releasing a wild horse into a large, open area is not a good idea, since you may not be able to recapture the animal.
Although there is competitive bidding, the adoption fee averages about $125 per animal. That's a bargain, but the BLM notes that the annual cost for maintaining a horse can easily exceed $1000.
You can find information, and an online adoption application at the BLM web site. And if you are interested in volunteering your time or money to help out with the Wild Horse and Burro program, you can find out how to do that there, too.