The term pacifism is used to describe a wide range of convictions. Finding a good definition would be a challenge, most likely we would end up with the classical 'psychiatrist definition' (ie 'Pacifism is defined as whatever people mean when they use the word') so we won't even try. That said, it generally means something along the lines of the belief that war is wrong under any circumstances, 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.
The first truly pacifist movement we know of is early Buddhism. The Buddha expected from his followers absolute abstention from any act of violence towards our fellow creatures. Despite the growth of Buddhism however, pacifism was not widely practised in Buddhist societies.
Jainism is a syncretistic1 religion with elements from Buddhism and Hinduism, and 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, in order that you can at least eat something.
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 unattainable ideal (it's a bit hard to survive without eating plants at the very least), but a person's failure to live up to it is balanced up by his good acts. Another thing that affects pacifist ideology is the pantheistic2 aspect of many Eastern religions - if you hurt others, you may literally be hurting yourself.
In the West, the first major pacifist movement was early Christianity. In the first centuries of Christianity, the church was verifiably pacifist, 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 pacifist, and perhaps for that reason there seems like there almost always have been pacifist groups in Christianity.
History in the West
The Reformation was a time of much ideological turmoil, and in this chaos there were also some groups who followed a pacifist ideology. Most noteworthy were the different Anabaptist groups. The Anabaptists ('re-baptisers') were called this because they rejected infant baptism.
These groups practised pacifism in a time of dire religious persecution. 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, in Germany, the Kingdom of Munster (1534-35) is established. And so now we're back in the middle ages, and the belief that '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 millennial totalitarian sect. To round it all off, when the Catholics recaptured the city of Munster, they celebrated with very messy and long-winded public executions of the Kingdom's leaders.
The poor ex-pacifists had probably 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 inspired by the mennonites, two other movements, German Pietism and English Quakerism, developed pacifist teachings virtually identical with the early anabaptists. Thus, there are several peace churches around today. Amish, Brethren, Mennonite and Quaker to name the most well-known.
Other prominent pacifist movements were the Bible students/Jehovah's Witnesses and the Antimilitaristic Workers' Movement. The Jehovah's Witnesses are very suspicious of worldly authorities, and since it's a pretty centralised 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. Unsurprisingly, this resulted in a lot of problems for them.
In the first half of the 20th Century the Workers' Movement was a really powerful movement that you didn't mess with if you were wise. Like the Jehovah's Witnesses, they were profoundly sceptical of governments. War and the military were seen as a means for oppressing the workers. Part of the Workers' Movement, like the war-weary German Pacifist Movement, were pacifist in the generally agreed-upon sense of the word. But some of those who refused military service had no qualms about using violence, as long as it was to overthrow the government they were so suspicious of!
If you are a member of one of the churches or secular groups that promote pacifist 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 (including France) have conscripted military national service, 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 conscientious objection to military service. If you're lucky, it's even legal in your country. Most industrialised countries now recognise 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 satisfactory 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 apartment. This at least shows that the conviction is there, but still peace tax has virtually no support outside the peace movement.