A modern commercial airliner can cruise at an altitude of 30,000 feets easily. However, Boeing 747 is certified to reach the altitude of 45,000 feet which is the maximum for any commercial jet. The problems which an airplane faces while at being extreme altitude are:
1> High-pressure difference
2> Low level of oxygen
When at high altitude there is an immense pressure on the airframe of the plane which could create serious flaws. The low level of oxygen is also a cause of concern as the engines burn fuel with oxygen and at high altitudes the level of oxygen is low. However, the service ceiling of the military jet is considerably higher than a commercial airliner.
The current record holder for the highest service ceiling is SR-71 AKA "Blackbird". It has reached the heights of 85,000 feets. But there are anomalies that come by flying at extreme altitudes, like:
1> The pilot cannot indulge in high-speed maneuvers as there is immense pressure on the plane airframe and doing such maneuvers could result in the breakdown of the plane. Thus most of the jets which fly at high altitudes are either spy planes or bombers especially designed to stand the high air-frame pressure.
2> The pilot needs to get into a special suit specially designed for these altitudes in order to keep the blood flowing in all vital body parts. There have been jets which have flown even to more than 100,000 feets but they merely qualify as jets and more as rockets.