Not all spiders are dangerous to humans. The spider usually injects its prey with venom kill the spider's prey, but because humans are a lot bigger than the prey that these spiders like to hunt, most spider venom usually doesn't kill (or even leave a noticeable mark) on a human unless the venom is especially strong. There are actually only a few spider species in the United States that would really hurt a person -- Here's a great visual list of common poisonous spiders:

Spider poisons usually have proteins that destroy cells through different mechanisms. Often times these poisons target specific functions or areas in the body, such as the nervous system.