Different types of servo horns are available with servos...  That made me wonder, if there are specific uses for each shapes?  Also about the holes on each of the axes of the horns. All I know as a newbie is that the sensitivity of the control changes depending how close is the hole selected to the control surface...
Maybe the experts around could enlighten new comers like me...

(The pic is taken from net just for reference)

Very good topic    This is something everyone needs to be well aware of 

Basically, the selection of arms for servos depend on a bunch of factors.  Here are some of them (others may add in).

1.  It has to be the proper arm for the type/make of servo.  This is the most important part. See our discussions:

http://www.rcindia.org/rc-general-topics/servo-arms/
http://www.rcindia.org/servos-gyros-and-all-electronics/the-importance-of-servo-arms/

2.  Length/size requirements/constraints. 

3.  The torque requirements for the intended application.

4.  Dual linkage rods - this means you have to use an arm with two sides.

5.  Throw required on the control surface.

Absolutely.  The selection of the hole depends on the throw needed on the control surface.  To get maximum throw (as an example, for 3D flying), one should use the outermost hole on the servo side, and innermost hole on the control surface end. 

But remember that "maximum throw that can be obtained" is NOT necessarily a good thing.  You should follow the recommendations in the build manual, or if you are scratch building, look at the physical constraints along with your style of flying.

I typically avoid the holes at the extreme ends (both inner and outer).