What is the maximum speed of modern commercial airliners?

 Today the fastest commercial jet, the Global 8000 can fly at Mach 0,94 , that's approximately 626 Knots TAS (1160 kph). With a hefty tailwind you can even go some 150+ knots (270 kph) faster over the ground. The modern commercial long distance aircraft are designed for best cruise at Mach 0.85 at roughly 35,000 feet MSL.

The maximum cruise is around Mach 0.90 at similar altitudes. The maximum cruise is limited due to selected airflows going transonic around the airfoil surfaces and causing increased drag.

Most large jet powered aircraft are limited to around .98 Mach since none are designed or built (or permitted) to exceed the speed of sound. The actual speed in knots or mph's varies with atmospheric conditions so a Mach limit is usually controlling.

The actual speed varies with altitude (faster as you get higher into less dense air) but generally, around Mach .92 to .95. At this high speed, the fuel consumption goes up dramatically so most airlines limit their speeds to around M .78 to M .85 or thereabouts, depending. As the upper surface of the wing and other surfaces approach the high end of the speed spectrum, the drag coefficient goes up and even in the transonic range, fuel consumption becomes an issue.

The speed at which a passenger jet can fly is limited by the faster air on the upper side of the wing which must at all costs be less than the speed of sound, or otherwise very dangerous phenomenons WILL take place. Normally the center of lift on a wing is at about 1/3 of the wing cord, but as you transit into sonic speed this center of lift will move aft, and as anyone can understand this will induce a pitch-down moment on the airplane.

Now that the Concorde is out of service there are no supersonic civilian aircraft. All remaining large commercial airliners and even regional jets can operate in the high subsonic range (>0.75 mach) at high altitudes.

Why do rich people choose to fly on private jets instead of airlines?

 One of the joys of being wealthy is being able to buy your way out of the inconveniences that the rest of us face. Flying private means you don't have crowded airports, long waits, the plane leaves on your schedule, no baggage claim carousel, no crying babies on the flight, lots of leg space and comfortable chairs, good food/beverages, total privacy and tons of time saved.

You call the company and tell them your address and destination address and just wait for the limo to arrive. It'll take you to the airport where the plane will take you to your destination and a limo at the far end takes you to the building you want.

No security, no lines - car to plane in five minutes. It's a custom-made nonstop flight on the right plane for the job. It also gives you a lot more options for airports as the airlines only serve a fraction of the available airports. If you fly commercial, getting to places like Vail, Jackson Hole, or Majorca can take two or three flights. With the right aircraft, you may be able to fly non-stop from Sardy Field to London City.

Most people who travel privately do it mostly for domestic travel. Many people will fly privately from their home city into a bigger airport and then catch their international connection on a commercial flight. You can instruct for inflight catering and it can be anything you can imagine. If it's international, you have to wait for a customs agent to board the plane, check and stamp your passport - you're now cleared through customs, right on the aircraft.

If you are a wealthy or famous person, there may be people who dislike you or who have mental or emotional issues that prevent them from controlling their behavior while on an airplane. With private jets, you do not have to worry about that. You can ensure that everyone on the aircraft is an employee of the company under some NDA.