Extended time traveling (at one time) increases a person's risk of developing Deep Vein Thrombosis (DVT). It occurs when people sit and travel on long flights, drives, etc. Blood is meant to flow, and when you sit for extended periods of time blood can become stagnant in the deep veins of your legs. DVT in and of itself is not going to cause you immediate danger. The danger comes when the clot, usually one that forms above the knee, breaks off and travels into your lungs (pulmonary embolism). This embolus can and does kill many people.
Symptoms occur when blood from the heart is blocked and back-up occurs in the leg. Watch for redness, swelling, pain and warmth. It is important to note that not all of these symptoms are present in DVT, so each symptom does not have to be present to have DVT. If there is also shortness of breath and chest pain, get to your doctor immediately. This could be a sign that the clot has broken and turned become the dangerous pulmonary embolism. If a clot has indeed formed in your leg, and it is caught early on, anticoagulant drugs may be administered with past medical history permitting.
If you will be traveling for a long period of time, make sure you drink plenty of water, get up frequently and move around a bit so your blood does not become stagnant. This will greatly reduce your risk of DVT.