Psychologically, how does volunteer work help the volunteer? This question has intrigued me for a long time, ever since I experienced it first hand (and continue to do so).  Some feel a compulsion to 'step up' and lend a hand to someone in need.  An example, after spending a day cleaning up a neighbour's flood ravaged business and then some time helping at an evacuation centre, I came home sore, bruised, bleeding, battered, utterly exhausted - but, I felt great - physically, I was a mess, but psychologically, I felt incredible.

What is/are bases for the psychological benefits often felt by volunteers?
Some of the "pay-offs" of altruism, but within the more extreme circumstance of risking one's life to save another are address in this answer.

In my opinion, volunteer work fulfills a person's needs to be useful, it also places a person in a position of superiority, as they are bestowing their "gifts" upon a "lesser" person in need. There is evidence that charitable work releases chemicals akin to pleasure in the brain. [Dan Schulman]

I cite Ferguson, Eamonn; Farrell, Kathleen; Lawrence, Claire :


  The benevolence hypothesis is supported, suggesting that blood donor
  motivation is partly selfish.


Citing  from the moral maze.


  "Even in human societies we can still trace many behaviours seemingly
  carried out for the benefit of the group back to benefits for the
  individual," Stanford explains.


In the study Altruism Costs - the Cheap Signal from Amygdala, it was demonstrated that there a neurological changes within the brain when contemplating making donations.


  neural processing of the cost-benefit difference. The presentation of
  a charitable donation goal evoked an insula activity that predicted
  the later decision to donate.../...   Our findings imply that the
  emotional system has an important role in real decision making as it
  signals what kind of immediate cost and reward an outcome is
  associated with.


So in summary, I believe the pay-off is a feeling of well-being, that is in accord with supporting the individual's self-esteem and some evolutionary theories of our instincts as a species.

The Biology of Benevolence
Humans may be hardwired to cooperate. The choice to cooperate stimulates pleasure centers in the brain.
By Dan Schulman,
published on November 01, 2002 - last reviewed on May 02, 2006

Blood donation is an act of benevolence rather than altruism.
Ferguson, Eamonn; Farrell, Kathleen; Lawrence, Claire
Health Psychology, Vol 27(3), May 2008, 327-336

Altruism Costs - the Cheap Signal from Amygdala.
Gospic K, Sundberg M, Maeder J, Fransson P, Petrovic P, Isacsson G, Karlström A, Ingvar M.