Coriolis effect and Cyclones
Don't think of the Coriolis force as deflecting motion clockwise/counter clockwise, but to the right (NH) or left (SH), when looking in the direction of the motion.

So this is sort of 'by definition'. A cyclone is a low pressure system, and air will move from a location with high pressure towards a location with low pressure. The Coriolis force will deflect this air to the right in the Northern Hemisphere, creating a counter-clockwise motion around the low pressure.
Around high pressure systems the direction of the motion is opposite, anti-cyclonic.

A very simple sketch, with a low pressure in the centre, and higher pressure around it:





Another way of looking at this is through the equation for geostrophic motion. The wind around a cyclone is (nearly) geostrophic, so the equation of motion can be simplified to 

$$
f\mathbf{k}\times\mathbf{v} = -\frac{1}{\rho}\nabla p
$$

where $f$ is the Coriolis parameter, $\mathbf{k}$ is the vertical unit vector, $\mathbf{v}$ is the wind speed vector, $\rho$ is density and $\nabla p$ is the pressure gradient.

So, looking at a sketch of a low pressure system on the northern hemisphere, the pressure gradient force will look like



The gradient itself goes from low to high pressure, but the force has the opposite direction. To achieve a balance between this and the Coriolis term, we need this situation:



(Note the negative sign for the Coriolis term here. In the above equation we have equality, so with the negative sign the direction is opposite that of the pressure gradient force.)

As $f$ is positive on the northern hemisphere, when we use the right-hand rule for cross-products, this means that $\mathbf{v}$ must be directed as



i.e., giving a counter-clockwise motion around the low pressure.