AMS - Acute Mountain Sickness - is a threat to your health, there has been a spike in the number of cases reported in the past year. Many trekkers have required emergency evacuation to lower altitudes.
Altitude sickness becomes a major risk above 2,400 meters (8,000 feet). Most people will feel short of breath as they acclimatise, however headaches, vomiting, difficulty sleeping, and the onset of pulmonary oedema or fluid on the lungs are serious symptoms
It is very important to acclimatise slowly and most guides will ensure you sleep at a lower altitude to the maximum reached in the day.
It is also important not to get dehydrated and to pace yourself.
Altitude sickness can be fatal and the onset of pink frothy liquid round the mouth and nose, breathlessness at rest, severe headaches, lack of co-ordination and vomiting should be treated as AMS and the person will need to descend rapidly. Descent is the only treatment for this very serious condition.
Any Himalaya trek out of Nepal, Bhutan, India, Pakistan is obviously a risk, but anywhere above 2,400 meters. Many people who land in Cusco, Peru intending to trek the Inca Trail become affected. The Atlas mountains in Morocco are also a risk zone. Kilimanjaro in Tanzania/Kenya is also responsible for a number of cases. Few of the European Alpine resorts are above 2,400 meters. However many resorts in the USA, mainly Colorado, are closer to 3000 meters.
Don't fly directly to a high altitude destination, stop off somewhere to acclimatise. Inca Trail trekkers should spend a day or two in Cusco (but be warned, it's high altitude anyway). Colorado skiers should acclimatise in Denver.
The rule for trekkers is 'climb high, sleep low'. So ascend to a new height during the day, but descend a little to sleep at night. The zig-zag route allows your body to adjust to the low oxygen pressure.
Don't take short cuts - if a guide suggests he can do an 8-day trek in 5, it's a sure sign he doesn't follow the 'sleep low' rule. Going straight up all day everyday is a recipe for disaster. If you don't have the time for a lengthy trek, make time, or pick a different trek.