Why is the deprotonated form of dopamine more reactive than the protonated/neutral form of dopamine? See this (from the Wikipedia article on dopamine):


  Dopamine, like most amines, is an organic base. At neutral or acidic
  pH levels it is generally protonated. The protonated form is highly
  water-soluble and relatively stable, though it is capable of oxidizing
  if exposed to oxygen or other oxidants. At basic pH levels, dopamine
  becomes deprotonated. In this free base form it is less soluble and
  also highly reactive and easily oxidized


I'm very curious about this since I'm curious about dopamine auto-oxidation, as it is often a cause of neurodegeneration observed in those who take amphetamines (and seems more likely in the cytosol, than the vesicles it would otherwise be in). Though I'm also curious how much auto-oxidation would happen for extracellular dopamine as well.
In general the free amine will react as a nucleophile i.e. by "donating" an available lone pair of electrons. In its protonated form, this lone pair is "blocked" and thus it has to lose a "blocking" proton to react (I use the words in "quotes" more freely - although I'm a chemist and not biochemist but hopefully it will help).

However re oxidation of dopamine, the reactive site is not the nitrogen (at least not the primary one - but will come back later) but the catechol part. Because of the electron donating effect of the 2 neighboring OH's, the aromatic ring is electron rich and more prone to oxidation to give o-quinone products. This oxidation reaction depends to an extend to the pH but mainly to the presence of (obviously enough) reactive oxygen species (ROS) and also enzymes (oxidases) or even Fe ions that can catalyse this oxidation. 

Coming back to the nitrogen, after oxidation occurs with creation of reactive sites on the quinone part, it can act now as a nucleophile and attack, creating indolines that will further oxidize to the more stable but toxic indole products.