Why do the boiling points of the hydrogen halides increase as you go down the group from HCl to HI?

That's a fantastic question. Here, we must consider two types of intermolecular forces as these are the attractive forces that affect the boiling point of a substance: van der Waals and permanent dipole permanent dipole forces. The H-X bond (where X=halide) is polarised, that is, the electrons in the covalent bond spend more time (on average) near the electronegative halide element. So, the bond becomes polarised delta+H and delta-X (where X=halide). This is the origin of the permanent dipole permanent dipole forces. As we go down from HCl to HI, the halide element becomes less electronegative. This means the bond become less polarised and the permanent dipole permanent dipole forces weaken. So why is the boiling point increasing? Well, as we are going down from HCl to HI, the size of the halide ion is increasing. Bigger ion=stronger van der Waals! So, the increase in van der Waals forces outweighs the decrease in permanent dipole permanent dipole forces.You may ask, why is the boiling point of HF so much higher than the rest of the hydrogen halides. The answer here is hydrogen bonding! When hydrogen is covalently bonded to a very electronegative element (F is the most electronegative), the bond becomes so polarised that the delta+H can form an electrostatic attraction to the lone pairs on neighbouring HF molecules: a hydrogen bond! This is much stronger than van der Waals and permanent dipole permanent dipole forces, giving an unusually high boiling point.