What is the armpit hair for?
I have been trying to read up a bit on this. I started out looking on wikipedia and it seems there are three hypotheses which are not necessarily mutually exclusive.

1.Aid the wicking of sweat away from the skin  

2.Reduce friction between the thorax and upper arm  

3.Facilitate the release of sex pheromones

The first would seem possible because it would help to prevent over-heating of the lymph nodes under the armpits and that also fits with the fact there are a lot of sweat glands there.

The second, I can't find any citations which support this but I understand that people who shave their armpits tend to suffer from dry underarms. This could be a result of increased friction.

The third is apparently controversial although it seems perfectly reasonable and highly likely to me. There is a famous experiment by Claus Wedekind who got men to wear a t-shirt for a few days. He then got women to choose a most preferred male purely by the scent of the t-shirt and found interesting results relating to the MHC profiles. The armpit hair could help to trap the odour produced by the sweat and help with mate attraction, like some kind of scent sponge. I don't understand why this is so controversial, loads of animals influence mate choice with scent - perhaps people don't like to think we are genetically attracted to each other by sweat because it seems animalistic and less romantic.

In summary, there is no sure answer and it could well be all of the above, or something entirely different.