Why is the acceleration due to gravity $g$ quoted as if it were constant? In elementary physics courses the value $g=9.8\:\mathrm{m/s^2}$ is used almost universally. But surely this value must depend to some extent upon one's location on the Earth. Why do we assume a constant value?
 A: To two significant figures, the acceleration due to gravity is $g=9.8\:\mathrm{m/s^2}$ everywhere on Earth (at sea level). That is to say, if you use e.g. a pendulum to measure $g$ to two sig figs, you will get this value no matter where you are. In a sense, this is the precision to which the Earth is well-approximated by a uniform sphere of matter.
The mean value is closer to $g=9.81\:\mathrm{m/s^2}$, which is also often quoted.
The third and fourth digits depends on exactly where you are on the Earth. They can nevertheless be predicted by assuming the Earth to be an "ellipsoid" rather than a sphere: the rotation of the Earth causes it to bulge outwards at the equator (since points a greater distance from the axis of rotation experience a greater centripetal acceleration). An ellipsoid can be characterized with two radii rather than one: the distance from the poles to the centre, and the distance from the equator to the centre.
The fifth and higher digits vary in more complicated ways. The (public domain) image below shows the difference between the actual gravitational acceleration at the surface - you can tell it is at the surface since for example the Andes are so red - vs. that of an ideal reference ellipsoid. These slight variations are due partly to the variations in density beneath the Earth's surface; i.e. if the ground beneath you has a lot of lead in it, its mass and therefore gravitational pull will differ compared to if it has a lot of water. Measuring these "gravitational anomalies" is one of the ways people detect good locations to search for oil, gold, etc.

Source
    http://earthobservatory.nasa.gov/Features/GRACE/page3.php 
A: Strictly speaking, $g$ (even more strictly speaking, $g_0$ or $g_n$) is a constant. It is exactly 9.80665 m/s$^2$, by definition. There are many places in science and engineering where it is very useful to have an exact (albeit arbitrary) defined constant for gravitation on the surface of the Earth. That said, gravitation on the surface of the Earth does vary, from about 9.78 ${\text{m}/\text{s}}^2$ atop a mountain near the equator to about 9.83 ${\text{m}/\text{s}}^2$ near the North Pole. That variation is not very important in introductory physics classes.
By focusing  on that variation you are missing an important lesson. By way of analogy, consider the biologist who only studies a particular ten-spotted species of beetles that only live on the north side of specific species of trees that only live on south-facing slopes in a certain type of forest. One day, that biologist sees beetles leaving a grove of trees in droves. "Are these my beetles?" he wonders. He focuses on counting the spots on the beetle's backs, and in doing so, he missed the reason the beetles were  streaming from the tree: The forest was on fire.
