Pacifism was huge in traditional Quakerism, to the point that their home countries (particularly England, where they started) would often get a bit angry with the Quakers for failing to participate in their wars.
However, over time, Quakerism as a whole has gotten much more liberal (relative to their starting-point, mind you), and it has become increasingly common for Quakers to join the military. Initially, their involvement was medical, but later expanded into combat. In doctrine, I think most Quaker churches still prefer pacifism, but it is not stressed nearly as much as it used to be.
The Biblical basis for their belief is a mixture of Matthew 5:9 ("Blessed are the peace-makers"), Matt 5:38-39 ("Turn the other cheek", although this is less military-related), and perhaps Matt 24:6-8 ("Wars and rumours of wars").
But their support comes mostly from the broad and very common theme throughout Scripture that all life is valuable, and we should love our neighbors and enemies. With these principles in mind, and a few steps of logic, they also have support from a few more ideas: that to take someone's life is to take away their chance to turn to God, that humans bear the image of God, that we should be more concerned with evangelizing and doing good works than the petty conflicts our governments get into, etc.