Why do only certain acids disassociate in water? I understand that most acids are weak acids, i.e. they do not fully disassociate in solution. However, certain acids, such as $\ce{H2SO4}$, do. I have been unable to find out what the defining characteristic is that differentiates strong acids from weak ones.

For example, HCl is strong, yet both HF and HBr are weak (even though they're based on halogens as well). Shouldn't HF be even stronger? 

What characteristic makes only a select few acids fully disassociate (and hence belong to the strong acid group)?
There are many factors that determine the strength of an acid:


electronegativity of the non-metal atom: an electronegative atom can attract more easily  the electrons of the hydrogen an so generate the proton.
atomic radius greater the radius of the conjugate base greater the acidity, this because the electrons are dispersed around the atom and there is a less attraction between the positive proton and the negative anion.
stability of the conjugate base if the conjugate base is stable due to some particular electronic configuration (e.g. stability due the resonance structure) the species are more prone to be dissociated.