What is pacifism?
The term pacifism isused to describe a wide range of convictions. Finding a good definition would be a challenge, most likely we'll end up with the classical "psychiatrist definition"1 so we don't try. But generally it means something like that war is wrong under any circumstance, that all violence and other coercive force is wrong under all circumstances, or that these things are wrong in by far the most circumstances. An example of the latter would be Gandhi's non-violence movement. Pacifists are often accused of merely being people who prefer fighting styles like Run-Lak Fekh. In fact there is a bit more to it.
Origins of pacifism
The first truly pacifist movement we know of is early Buddhism. The Buddha expected from his followers absolute abstention from any act of violence toward our fellow creatures. Despite the growth of Buddhism however, pacifism was not widely practiced in buddhist societies in general.
Jainism is a syncretistic2 religion with elements from Buddhism and Hinduism, in this movement non-violence is taken very seriously. Non-violence is here extended to all living things including insects and plants, but in practice, of course, you are only expected to make a reasonable effort.
At the core of eastern non-violent ideology lies the belief in reincarnation and karma. According to these teachings, what you do in this life will come back to you in later lives. A consequence of this is that for example among jains the actual teaching is an unnatainable ideal3, but a person's failure to live up to it is balanced up by his good acts. Another thing that affects pacifistic ideology is the pantheistic4 aspect of many eastern religions - if you hurt others, you may literally be hurting yourself.
In the west, the first major pacifistic movement was early christianity. In the first centuries of christianity, the church was verifiably pacifistic, and all the church fathers who spoke on the issue revealed pacifist teachings. Around the third century, this changed as christians for the first time killed each other over theological disagreements. In his "Confessions" the church father Augustine (354-430 AD) advocated that war was acceptable to defend the church, and this is often seen as the beginning of the "just war" doctrine.
However, there are passages in the gospels that certainly seem pacifistic, and perhaps for that reason there seems like there almost always has been pacifistic groups in christianity.
History of pacifism in the west
The reformation was a time of much ideological turmoil, and in this chaos there were also some groups who followed a pacifistic ideology. Most noteworthy were the different anabaptist groups. The anabaptist ("re-baptisers") were called this because they rejected infant baptism.
These groups practiced pacifism in a time of dire religious persectution. One of the consequences was that leaders often had a very short life expectancy. Perhaps in frustration with this the non-pacifist elements became stronger. Imagine: first they say they will only fight at Armageddon, then they become increasingly convinced Armageddon is close at hand, because frankly they are tired of being persecuted all the time. Now after a couple of revelations things turn nasty, and the Kingdom of Munster(1534-35) is established. We're back in the middle ages, and "God will punish you for what you've done to us" has become "We will punish you on God's behalf because of the things you've done to us". The result is a millenialistic totalitarian sect which makes Jonestown look like summer camp. To round it all off, when the catholics recaptured the city, they celebrated with very messy and long-winded public executions of the Kingdom's leaders.
The poor ex-pacifists probably had had enough violence for several generations, so when the wandering anabaptist preacher Menno Simons preached a return to the movement's pacifist roots, quite a few followed him. Menno united many Munster survivors with the ones who had remained pacifist all along. Their descendants are still around, they're the Mennonites, a pacifist church to this day.
The Mennonites influenced others early on, and they had some minor schisms. In addition, and perhaps inspered by the mennonites, two other movements, german pietism and english quakerism, developed pacifistic teachings virtually identical with the early anabaptists. Therefore there are several peace churches around today. Amish, Brethren, Mennonite and Quaker to name the most well-known.
Other prominent pacifistic movements were the bible students/Jehovahs witnesses and the antimillitaristic workers' movement. The Jehovas Witnesses are very suspicious of worldly authorities, and since it's a pretty centralized church, all members everywhere are forbidden to take part in war. Even more controversially, for a long time the Watch tower society also forbade witnesses to take alternative service. Unsuprisingly this resulted in a lot of problems for them.
In the first half of the twentieth century the workers' movement was a really powerful movement you didn't mess with. Like the Jehovas' Witnesses they were profoundly sceptical of governments. War and the millitary was seen as a means for opressing the workers. Part of the workers' movement, like the war-weary german pacifist movement, were really pacifistic in the generally agreed-upon sense of the word. But some of those who refused millitary service had no qualms about using violence - as long as it was to overthrow the government they were so suspicious of!
Politics of pacifism
If you are a member of one of the churches or secular groups that promote pacifistic ideals, then you might very well disagree with your government on some issues. The first and most serious is perhaps conscripted military service. Today many countries have conscripted military, which means that all men (and, in Israel, women) must serve in the military for some time. This should disturb you if you're a pacifist. Worse, even those countries that don't have a conscripted army usually have a draft in wartime.
The solution is conscientous objection to military service. If you're lucky, it's even legal in your country. Most industrialized countries now recognize the right to do alternative service of some sort instead of military service. In the past pacifists used to get away with paying a special tax, but this was not seen as a satisfying solution, since you're in essence paying someone else for doing what you won't do yourself. Some have taken this further, and say that since our present military is so dependent on equipment rather than people, we must have some option of not supporting it economically either. A peace tax has been proposed, where the part of your tax that would ordinarily go to the military budget instead goes to a fund for protecting the country in non-violent ways. So far no country has implemented a peace tax, but there are actually many people in the US who demonstrate for it by living below the taxable level - that's pretty low, you have to do without a car and apartement. This at least shows that the conviction is there, but still peace tax has virtally no support outside the peace movement.