For most visitors, travel to Machu Picchu is quite safe. You will need to be much more vigilant when traveling through large cities such as Cusco and Lima. Due to a large number of taxi-related 'express kidnapping' (in which a victim is kidnapped, immediately taken to an ATM or bank to get money, then released), it is better to never get in an unregistered cab, and best to order a cab by telephone, rather than hail a cab on the street.

Such issues within Machu Picchu and along the Inca Trail, however,  are nonexistent. As with any locale you are unfamiliar with, it pays to be alert while traveling within large crowds, especially during the high season. Pickpockets can quickly pick you clean of your money or passport, quickly turning a dream vacation into a nightmare. Make use of your hotel's safe to protect items such as any jewelry you might have brought with you (which, in reality, is best left at home), extra monies, credit cards, and passports. Keep an eye (and hand) on bags at all times, and do not leave your items unattended.

If planning to hike along the Inca Trail to Machu Picchu, bring along plenty of water and sunscreen. The hiking trail is quite exposed and is very strenuous in spots. Be aware that high altitude sickness can be a problem. Allow yourself to acclimate and do not push yourself if you begin to feel sick.

Keep a copy of the front page from your passport, any tickets, credit card numbers (and 800 numbers in case cards are stolen), and any other important information in a location separate from the originals. These will come in handy if you are a victim of theft.  

For up to date issues in regard to travel to Machu Picchu and Peru, check ou the US Consulate Information sheet for Peru.