What would be the purpose of a manned mission to Pluto?
Like any intra-Solar exploration, the dwarf planet of Pluto (downgraded from planetary status in 2006) offers unique opportunities for scientific research, mineralogical study, and human expansion. While the last is a long time in the future, due to technological limitations, the other two could provide new information about the origins of the Solar System as well as the effects of Pluto's climate and distance from the Sun on experiments.
As Humanity expands into the Solar System (likely within the next hundred years), colonization of other planets will become a vital part of research and development. After colonies are established on closer planets, a manned mission to Pluto will become inevitable, if only so someone can be the first to walk on its surface. Human colonies on Pluto's surface will be problematic because of the low Solar radiation, intense cold, and general lack of resources; a colony will need to be entirely self-sufficient without dependence on external resupply. This eventuality will offer interesting opportunities to research how humans cope with low gravity, an intensely hostile environment, and distance from other humans for long periods of time, to an extent far greater than similar data gathered from the International Space Station.
Another possibility for a manned mission would be to attempt changing the orbit of Pluto to bring it into the Inner Solar System. At about two-thirds the size of the moon, Pluto is likely to contain many thousands of tons of valuable resources, which may be important in Earth's continuing vitality. Similar missions will attempt to move asteroids earlier, but the movement of Pluto -- at the cost of enormous time and expense -- would provide far more resources than most asteroids. This sort of mission is far in the future; possible missions in the near future would simply be to examine the composition of the planet for future decisions.
The spacecraft New Horizons will pass by Pluto in 2015 closer than any other spacecraft, allowing better understanding of the conditions and composition of the dwarf planet.