How High is Cusco, Peru?
Cusco is located at an elevation of 11,152 feet (3,399 meters) above sea level.
At this altitude, you'll probably notice that relatively simple physical activities, such as walking through the streets of Cusco or carrying your backpack up hostel stairs, become more difficult and soon leave you short of breath (so spare a thought for soccer players playing at Cusco's Estadio Garcilaso).
You should always take time to acclimatize when you arrive in Cusco.
Allow at least 24 hours for acclimatization, or two days if possible. If you don't acclimatize properly, you will be far more susceptible to altitude sickness (read more about altitude sickness in Peru here, including prevention and symptoms).
If you're in Cusco to visit Machu Picchu, you'll be happy to know that Machu Picchu is at a lower altitude (7,972 feet, or 2,430 meters). If you take the time to acclimatize correctly in Cusco, you should have few problems with altitude at Machu Picchu.