Appropriate Attire -- Many travelers to Peru are dressed head-to-toe in adventure or outdoor gear (parkas, fleece wear, hiking boots, and cargo pants). This is perfectly acceptable attire for all but the fanciest restaurants, where "neat casual" would be a better solution. In churches and monasteries, err on the side of discretion (low-rise pants, midriff shirts, peekaboo thongs, and anything else that reveals a lot of skin are not usually acceptable).
Avoiding Offense -- In Peru, you should be tactful when discussing local politics, though open discussion of the corruption of past presidents and terrorism in Peru is perfectly acceptable and unlikely to engender heated debate. Discussion of drugs (and coca-plant cultivation) and religion should be handled with great tact. Visitors should understand that chewing coca leaves (or drinking coca tea) is not drug use but a long-standing cultural tradition in the Andes.
In a country in which nearly half the population is Amerindian, expressing respect for native peoples is important. Try to refer to them not as indios, which is a derogatory term, but as indígenas. Many Peruvians refer to foreigners as gringos (or gringas) or the generic "mister," pronounced "mee-ster." Neither is intended or should be received as an insult.
On the streets of Cusco and other towns across Peru, shoeshine boys and little girls selling cigarettes or postcards can be very persistent and persuasive. Others just ask directly for money (using the euphemism propinita, or little tip). The best way to give money to those who are obviously in need of it is to reward them for their work. I get my scruffy shoes shined on a daily basis in Peru, and I buy postcards I probably don't need. If you don't wish to be hassled, a polite but firm "No, gracias" is usually sufficient, but it's important to treat even these street kids with respect.
Queries about one's marital status and children are considered polite; indeed, women traveling alone or with other women should expect such questions. However, discussion of how much one earns is a generally touchy subject, especially in a poor country such as Peru. Although Peruvians might be curious and ask you directly how much you make, or how much your apartment or house or car or even clothes cost, I suggest that you deflect the question. At a minimum, explain how much higher the cost of living is in your home country, and how you're not as wealthy as you might seem. Ostentatious display of one's relative wealth is unseemly, even though Peru will be blissfully inexpensive to many budget travelers.
Shopping -- Bargaining is considered acceptable in markets and with taxi drivers, and even hotels, but only up to a point -- don't overdo it. Also bear in mind that many shops in large and small towns close at midday, from 1 to 3pm or 2 to 4pm.
Gestures -- Peruvians are more formal in social relations than most North Americans and Europeans. Peruvians shake hands frequently and tirelessly, and although kissing on the cheek is a common greeting for acquaintances, it is not practiced among strangers (as it is in Spain, for example). Amerindian populations are more conservative and even shy. They don't kiss to greet one another, nor do they shake hands as frequently as other Peruvians; if they do, it is a light brush of the hand rather than a firm grip. Many Indians from small villages are reluctant to look a stranger in the eye.
Using your index finger to motion a person to approach you, as practiced in the United States and other places, is considered rude. A more polite way to beckon someone is to place the palm down and gently sweep your fingers toward you.
Greetings -- When entering a shop or home, always use an appropriate oral greeting (buenos días, or good day; buenas tardes, or good afternoon; buenas noches, or good night). Similarly, upon leaving, it is polite to say goodbye (Adios or Hasta luego), even to shop owners with whom you've had minimal contact. Peruvians often shake hands upon leaving as well as greeting.
Photography -- With their vibrant dress and expressive faces and festivals, Peruvians across the country make wonderful subjects for photographs. In some heavily touristed areas, such as the Sunday market in Pisac outside of Cusco, locals have learned to offer photo ops for a price at every turn. Some foreigners hand out money and candy indiscriminately, while others grapple with the unseemliness of paying for every photo. Asking for a tip in return for being the subject of a photograph is common in many parts of Peru; in fact, some locals patrol the streets with llamas and kids in tow to pose for photographs as their main source of income. Often it's more comfortable to photograph people you have made an effort to talk to, rather than responding to those who explicitly beg to be your subject. I usually give a small tip (50 centavos to S/1, or 35¢) if it appears that my camera has been an intrusion or nuisance, or especially if I've snapped several shots.
It's not common except in very touristed places (such as the Pisac market), but some young mothers carrying adorable children in knapsacks and with flowers in their hair (and outstretched hands requesting a propinita, or tip) aren't actually mothers (or at least, not the mothers of the children they're carrying around); to tug at your tourist heartstrings and pockets, they have essentially "rented" the babies from real moms in remote villages. I don't think it's an especially good idea to reward this practice. If a very young woman has several children in tow, all dolled up for pictures and making the rounds all afternoon, she is very likely one of these rent-a-moms.
Photographing military, police, or airport installations is strictly forbidden. Many churches, convents, and museums also do not allow photography or video.
Punctuality -- Punctuality is not one of the trademarks of Peru or Latin America in general. Peruvians are customarily a half-hour late to most personal appointments, and it is not considered very bad form to leave someone hanging in a cafe for up to an hour. It is expected, so if you have a meeting scheduled, unless a strict hora inglesa (English hour) is specified, be prepared to wait.