What is the acceleration caused by gravity of the planet earth?

The general accepted value of acceleration due to gravity, g, is 9.81 m/s^2.

That is an approximation because being the acceleration of gravity due to the attraction of the earth its magnitude will depend on the distance from the point to the center of the planet Earth.

The value of g is determined by using the Newton's Universal Law of gravity:

F = G * m of Earth * m of body / (distance^2)

Wehre {G* m of Earth / (distance^2) } = g

G is a universal constant = 6.67 * 10 ^ -11 N*m^2 / kg^2

m of Earth = 5.98 * 10 ^ 24 kg 

distance = radius of Earth + height of the body

Given the the Earth is not a perfect sphere the radius varies. Also the height of the body varies.

If you take a mean radius of Earth of 6.37*10^6 m

you get

g = 6.67*10^-11 N*m^2/kg^2 * 5.98*10^24kg / (6.37*10^6 m)^2 = 9.83 m/s^2

Again, if you want a more precise value of g, you need to find the exact place where you are and then use the right r.