Stay safe & healthy
The country has a reputation as a risky destination in some circles (primarily Australian ones), predominantly because of the activities of criminal gangs (known in Tok Pisin as raskols) in major cities, especially in Port Moresby and Lae.
That is generally a result of unemployment stemming from increased domestic migration from subsistence farming in the hills to the nearest urban area.
There is no history of heavy settlement in the Port Moresby and Lae areas. Hence, they are colonial cities comprised of a mix of tribal people which fosters instability. Madang, Wewak, Goroka, Mt. Hagen, and Tari are much safer with longer periods of settlement and a more stable tribal homogeneity.
The villages are quite safe as the locals will "adopt" you as one of their own.
If you must, the most important thing is to stay up to date on the law and order situation in the locations you are planning to visit.
Most hotels in Port Moresby are secure and situated inside compounds, generally with guards patrolling the perimeter. However, actual gunfire in the capital is mercifully rare. If you plan on taking a tour of any city, make inquiries with your hotel or accommodation provider, as many will be able to either walk with you or drive you to wherever you are planning to go, or just around the local area if that is what you want to do.
Avoid going out after dark, but if you must, stay very alert.
Flying in small planes can be very risky. Hardly a year goes by without at least one fatal accident (the most recent in August 2009 when 12 people were killed). While the planes are usually well-maintained and the pilots technically proficient the problem is the mountainous terrain. Many smaller airfields are situated in steep valleys. When there is cloud cover planes have difficulty in finding them and sometimes crash into a mountain. The national airline, Air Niugini, which flies internationally and to the major cities of the country has, however, an unblemished safety record in 32 years of operation.
Saltwater crocodiles (Crocodylus porosus) are common in Papua New Guinea and are capable of growing to immense lengths of 7 m or more (although individuals over 6 m are rare). They occasionally devour humans. They are equally at home in coastal waters as they are in freshwater lakes and rivers. Avoid swimming except at higher elevations and in hotel swimming pools. Papua New Guinea, along with Australia, has the highest and healthiest population of large saltwater crocodiles in the world.
Papua New Guinea is home to many active volcanoes and several of the most popular treks involve getting close or actually climbing one or more of these. Always heed local advice and a regular check of The Smithsonian Institute's Volcanic Activity Report would be wise.
Tap water in some regions can be unsafe to drink.
Malaria can be a hazard as well, although many villages, particularly those connected to industry, are regularly treated for mosquitoes. Take the appropriate precautions against mosquitoes and mosquito-borne diseases.
Malaria medication can be purchased at the pharmacies and, in addition to warding off malaria, will keep your stomach happy as well.