According to the experiments done and currently verified, in vacuum (this means there is not air or any fluid), all objects in free fall experience the same acceleration, which is the acceleration of gravity.
Now, in this case we are on Earth, so the gravity value is [tex]9.8\frac{m}{s^{2}}[/tex]
Note the objects experience the acceleration of gravity regardless of their mass.
Nevertheless, on Earth we have air, hence air resistance, so the afirmation "Free fall is a situation in which the only force acting upon an object is gravity" is not completely true on Earth, unless the following condition is fulfiled:
If the air resistance is too small that we can approximate it to zero in the calculations, then in free fall the objects will accelerate downwards at [tex]9.8\frac{m}{s^{2}}[/tex] and hit the ground at approximately the same time.