Besides the general safety advice offered in each country section, women traveling alone in South America should have few problems. Yes, in many cultures here, men have a very macho attitude, and women traveling alone can expect to get intense stares, catcalls, or even be followed for a few blocks by men asking for a date. But for the most part, these men are harmless. A simple "Déjame en paz" ("Leave me alone") will send the message that you're not interested.
There have been sporadic, unconfirmed reports of tour guides attacking single women travelers. It's always worth it to pay a few extra dollars to arrange a tour with a reputable travel agency. Talk to your fellow travelers and find out if they have had any problems. If you are attacked, contact the police immediately and notify your embassy. Safety specialists at your embassy will be able to assist you and hopefully work with the police to track down the assailant.
Several websites offer women advice on how to travel safely and happily; a good one to check out is Journeywoman (www.journeywoman.com), a "real-life" women's travel information network where you can sign up for a free e-mail newsletter and get advice on everything from etiquette and dress to safety. If you'd rather not travel alone, consider Women Welcome Women World Wide (5W; tel. 203/259-7832 in the U.S.; www.womenwelcomewomen.org.uk), which works to foster international friendships by enabling women of different countries to visit one another (men can come along on the trips; they just can't join the club). It's a big, active organization, with more than 3,500 members from all walks of life in some 70 countries.