How fast does the average commercial passenger jet have to go to take off?

The answer to this depends on what speed you are talking about. Aircraft work in airspeed - the speed of the aircraft in relation to the air around it. Ground speed is a function of these two things.

An aircraft's performance is based on its airspeed, just as Anguilla said. So most aircraft can take off at around 150kts airspeed (about 170mph), some slower, some faster. What this equates to on the ground, though, is dependent on wind speed.

Wherever possible, an aircraft will always take off and land into the wind.

Example: an aircraft is facing into 20kt winds. At its current weight, the aircraft has a takeoff speed of 140kts. For it to reach 140kts airspeed, it will need to be doing 120kts groundspeed. This, plus the 20kt headwind will give it a total airspeed of 140kts.

The same plane taking off with the wind (facing away from the wind) would need to build up a ground speed of 160kts to overcome the 20kt tailwind.

Q: What speed do large passenger jetliners usually build up to on the runway before they take off?

A: Jetliners typically takeoff at 160 to 180 mph (260 to 290 km/h), though it depends on how heavily the plane is loaded and whether the pilot is using flaps or slats. These devices increase the plane's lift so it can take off at slower speeds.

When I say "speed" I mean airspeed (relative to the air). So, theoretically, a plane could just sit there and take off into a 160 mph wind. It would take a strong hurricane to create this wind.

Airspeed is critical because it provides lift. That's why planes take off into the wind: to maximize airspeed. The wind hits the up-tilted wings and tail and flows down — the path of least resistance. The air exerts an equal and opposite-upward-force on the wings and tail. The plane rises due to this lift.

Aircraft carriers maneuver so their deck is pointed into the wind as much as possible when launching and retrieving fighter planes. They catapult 45,000-pound planes (20,400 kg) into the sky at takeoff speeds of 165 mph (266 kg/h)-reaching those speeds in two seconds!

---http://www.usatoday.com/news/science/wonderquest/2003-07-18-wonderquest_x.htm

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