Boeing 737 usually takes off right around 150 MPH. It's also interesting that the acceleration rate is actually quite slow. It picks up speed more gradually than you'd think. Takeoff speeds vary tremendously from one aircraft to the next, and also can change for the same aircraft from one flight to the next based on such factors as the density altitude and the aircraft's weight.
Takeoff speed is determined by a number of factors including the specific type of aircraft, how heavily the aircraft is loaded, flap settings, length of the runway, and altitude of the takeoff airport. The weather can also have an impact as pilots may wish to take off at a higher speed in case of a sudden change of wind direction and resulting tailwind.
For smaller regional jets, takeoff is in the range of 115 to 130 knots. For aircraft such as Boeing 737 and Airbus A320 family, takeoff is in the range of 130 to 150 knots. For mid-size aircraft such as Airbus A330 and Boeing 757/767/777/787, takeoff is in the range of 140 to 165 knots. For larger double deckers such as Boeing 747 and Airbus A380, takeoff is in the range of 145 to 175 knots. Just as a sidenote, Concorde took off at around 200 knots with no flaps when fully loaded.
Most of the time, commercial aircraft with passengers on them will take off around 5 to 10 knots faster than the absolute lower limit for that configuration. This is just to allow the pilot to correct an excessive pitch up or incorrect power setting before it results in a classic departure stall. Takeoffs are broken down into several different speeds called V1, Vr, and V2. V1 is known as the decision speed because this is the speed at which you must commit to takeoff because there isn't enough runway to stop in time. Vr is the rotation speed and is the speed at which the pilot should begin to pull up off the runway. V2 is the safe takeoff speed, and once in the air V2 is the speed that means if an engine failure is suffered the aircraft can continue to climb.
Weight alone has little to do with takeoff speed. The design of the wing doing the lifting is much more important. That's why both an Airbus A340 and a Boeing 747 weighing half again as much take off at about 155 knots under normal conditions from a near-sea level airport.