Peru continues to be a very macho, male-dominated society. Although women are a growing part of the professional workforce and a relatively recent feminist movement is evident in urban areas, women do not yet occupy the (still unequal) position they do in many Western societies. Still, women should not encounter any insurmountable difficulties traveling in Peru.
However, women should not be surprised to encounter perhaps unwelcome attention from men, especially if traveling alone. Many Peruvian men consider gringas -- essentially, any foreign women -- to be more sexually open than Peruvian women; thus, foreigners are frequently the targets of their advances. Blonde women are frequently singled out. Piropos, come-ons that are usually meant as innocuous compliments rather than as crude assessments of a woman's physical attractiveness or sexuality, are common in Latin America. However, comments can occasionally be crude and demeaning, and groping is not unheard of in public places (such as on crowded buses). Sexual assaults are rare, but the threat felt by some women, especially if they do not comprehend the Spanish slang employed in come-ons, is understandable.
Many men, as well as Peruvian women, might be curious about why a woman isn't married or traveling with a boyfriend. A woman traveling alone could elicit comments of sympathy or even pity. Wearing a ring on your wedding finger and deflecting comments and advances with a story about your husband working in Lima and meeting you in 2 days (or something to that effect) could be a useful tactic. In general, the problem is much more pronounced in large cities than in small towns and the countryside. Amerindian populations are conservative and even shy in dealing with foreigners, including women.
Women on the receiving end of catcalls and aggressive come-ons should do what Peruvian women do: Ignore them. If that doesn't succeed, contact the tourist police. Although some Peruvian men might be innocently interested in meeting a foreign woman, it is not a good idea to accept an invitation to go anywhere alone with a man.
Women traveling in a group with other females, or especially with a man, are less likely to attract unwanted attention from men. Although I would hesitate to tell a woman friend that she should not travel alone in Peru, traveling with even one other woman might feel like a safer situation for many women, at least psychologically. If you are traveling alone, never walk alone at night anywhere -- always call for a registered taxi. It's also a good idea to have a whistle handy; a piercing sound blast will deter almost any aggressor.