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 are parachutes not used on commercial planes?

 You're asking a group of untrained members of the public to strap on a device they have zero training with, and figure out how to exit a plummeting jetliner, without hurting themselves. Passengers are not trained to use parachutes, which contrary to popular belief, involves more than just pulling the cord.

Some people are physically incapable of landing using a parachute safely, for example old people, kids, people with physical disabilities. Parachutes are tailored based on your weight, so what works for one person might not be enough for another. A study of all commercial airline accidents between 1983 and 2000 found that 95.7% of the people on board survived, which means staying with the aircraft is almost always the better option.

There is no convenient way to jump out of typical airliners. Just jumping out of normal side-facing airplane doors or emergency hatches, you would probably hit the wing or the tail. Exit airspeed would need to be 200 mph or less, but commercial jets fly at 500+ mph. Jumping from altitudes of more than 20,000 feet can cause hypoxia, unless you have oxygen to take with you. Most accidents occur at take-off and landing, where parachutes are of no use anyway.

Parachutes are bulky, heavy and expensive. They would not even fit under your seat, they would occupy a lot of space and add a lot of weight. They would also need regular inspection and repacking. To provide several hundred per airplane would add significantly to costs, making flying much more expensive.

Furthermore, accidents that result in deaths are usually the result of sudden catastrophic failure. The kinds of failure that do not allow for people to properly strap on a chute, bring the plane to a proper speed and altitude, and hold that speed and altitude while the passengers jump off in an orderly manner. Nearly every single accident out there is better managed by putting the large metal tube in the hands of a skilled pilot, and attempting to bring the whole thing down in as safe a manner as possible.