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.