There is such a thing as centrifugal force, but it's a misnomer; the phenomenon isn't a force at all. Rather, it's a mathematical fudge factor introduced by physicists when they want to use Newton's laws of motion in a rotating, non-inertial reference frame. Newtonian mechanics is only valid in frames of reference that are either stationary or moving with constant velocity (according to relativity theory, there's no difference between the two anyway). Imagine a marble on a rotating platform on a table. In attempting to describe this situation, one traditionally chooses a coordinate axis attached to the table, which is not accellerating, and compares the marble's movement-resisting inertia with the centripetal force of friction between the marble and the platform to determine where the marble will go. Unfortunately, this can be conceptually difficult. The alternative, often discouraged in introductory physics courses but allowed later on, is to choose a coordinate axis rotating relative to the table, and attached to the platform. Newton's classic equations will not work in this reference frame because it is accellerating, but they can be made to work by treating it as if it weren't. To do this we have to introducing a virtual outward-pointing force, the centrifugal force. A derivation of the centrifugal force using vector calculus follows.

F=mAi
Newton's Second Law in an inertial reference frame.

(d/dt)i=(d/dt)r+(w x r)
Apply this coordinate transformation...

Vi=Vr+(w x r)
...to the radius vector.

(d/dt)i=(d/dt)r+(w x r)
And again...

Ai=Ar+2(w x Vr)+(w x (w x r))
...to the velocity vector.

Fi-2m(w x Vr)-m(w x (w x r))=mAr
Substitute into the initial Second Law equation...

Feff=Fi-2m(w x Vr)-m(w x (w x r))
...and get the effective force.

The third term on the right, -m(w x (w x r)) is the centrifugal force.
The second term on the right is the icing on the cake. -2m(w x Vr) is the Coriolis force.