Back in the early 2000s, a case emerged where 30 people were suing airline companies due to suffering from Deep Vein Thrombosis while flying. This is a clot that forms due to inactivity. The danger of these clots is increased by general health factors. Obese people and those with heart disease are at higher risk. The key is to avoid being inactive for the entire flight. Stretch your legs or get up and move around at least every two hours and your risk of DVT is greatly reduced. It is the seated immobility of a long flight that increases DVT risk.
When flying, you may have access to slightly lower levels of oxygen in the air compared to normal. For most people this isn't a problem, especially over a short distance. For those with heart or lung problems, this is more serious, especially when it goes on for hours on end. Asthma sufferers should make sure to carry medication such as an inhaler with them on the flight in case they have difficulty breathing.
Jet lag makes many people feel tired, confused and generally unable to function well after a very long flight. The more time zones you cross, the more you disturb the natural circadian rhythms that keep your body on track. More physical symptoms such as nausea and gastrointestinal problems can also arise from jet lag. General good health, avoiding caffeine and staying hydrated all help alleviate jet lag. Also, if you can adjust your sleeping schedule a few hours for a few days before you leave on your trip, your body will be in a rhythm a few hours closer to what it needs to be after reaching your destination. This makes the adjustment more comfortable.
Some people experience a condition known as air rage. This is similar to road rage where a person loses control of his temper. In the case of air rage, it can be caused by exhaustion, drinking too much on the plane or even due to symptoms caused by the lack of oxygen and changes in pressure. However, a common target of air rage on long haul flights is heavy smokers who are without nicotine for long periods of time and are prone to fits of rage.