Mr. Chance, you as sooo getting coal in your Christmas stocking for asking this question. 
Neener neener! I’m a Jew!
I was raised Lutheran (and now I’m a devout infidel), but I’m not a theologian, so don’t expect me to get everything right. The main difference between the Lutherans and the Catholics is the Lutheran idea of salvation through grace alone. The Lutheran denomination dates back to Oct. 31, 1517, when Martin Luther, angry at the Catholic sale of indulgences, posted 95 theses, or arguments against this practice, on the door of Wittenberg Cathedral in Germany. Luther originally wanted to merely start a debate that would lead to reform in the Church, but the conflict eventually led to his founding his own religion.
The idea of salvation through grace is basically that, since all humans, no matter how righteous, are sinners, it is only through God’s grace that they can be saved. This grace can only be attained through faith in Jesus. Other differences from Catholicism include less Biblical books (Luther decided that the Apocrypha weren’t essential), more emphasis on an individual relationship with God, rather than one mediated through a priest (although clergy still do have a specific function), and only two sacraments, those of baptism and communion, eliminating the idea of confirmation, confession, last rites, ordination, and marriage as sacraments.
As for tolerance for other Christian sects, Lutherans believe that everyone who truly believes in Jesus as the Son of God and Savior is a Christian (and will go to heaven, being saved by Jesus). This is more inclusive than the Catholic Church (I don’t know about their beliefs regarding who is a Christian, but they don’t generally allow non-Catholics to take Communion with them, while Lutherans let all Christians do it).
Lutheranism is also divided between smaller synods, such as the ELCA and LCMS, which differ on some points (the LCMS is generally more conservative than the ELCA, for example).
Any errors in the above post should be attributed to ignorance rather than malice.
That can be a definite understatement. While I’d argue that all three synods in the US–Wisconsin, Missouri, and ELCA (Evangelical Lutheran Church of America)–are fairly conservative, there are some definite doctrinal differences. The ELCA is easily the most liberal when it comes to doctrine. I know several women ELCA pastors (well, I know of, though I’ve never really met more than one or two), which would basically never happen in the other two synods, especially Wisconsin.
(I was raised ELCA Lutheran, and while I’m not all that religious, I find it to be a rather good compromise as religions and denominations go.)
In my post above, I tried to explain some of the history of the United Methodist church. I didn’t get all of it correct. Here’s a website about the history of the United Methodist church, starting from its origin in English-speaking churches in the early history of the U.S. as Methodists and in German-speaking churches in the same time as Evangelicals and United Brethren:
http://www.umc.org/abouttheumc/history/
Even this doesn’t mention everybody today who calls themselves a Methodist. As Lilith Fair mentioned, there are also Free Methodists, who broke off from the Methodists a century and a half ago. Jonathan Chance, would it suffice to say that you’re never going to get a coherent explanation of the diversity of Christian groups from the answers in a SDMB? You really need to read a book to understand this.
There are about 32,000 Christian denominations, though probably that number is inflated somewhat.
I did a post recently at the Pizza Parlor that included a bunch of links to lists of denominations; I’ll C&P it here:
Links to Websites of Major Denominations (and some not so major)
Religious Tolerance.org’s breakdown of denominations
Another bunch of links to denomination websites. And yet another one. And yet more.
Approximate membership of some denominations.
Some examples of unusual groups:
[ul][li]The Schwenkfelders: a completely separate tradition with six churches and about 4,000 members. [/li]
[li]The website of the National Association of Free Will Baptists. [/li]
[li]The Duck River Baptist Association. These guys were an independent, separate denomination some years ago; based on their affiliation with the Tennessee Baptist Convention, it appears they may have made their peace with the Southern Baptists.[/li]
[li]the Metropolitan Community Churches.[/ul][/li]
Getting into whygroup Y split off from group X is pretty complex. Poly gets prolix on the origins of Christian denominations, over on the Pizza Parlor (I quoted much of this in a GD thread here as well.)
Alleluia
(Fixed links (I think)–TVeblen
And I think I fixed the"Approximate membership of some denominations".
I’ll add one denomination to the list I don’t think most of you have even heard of – my best friend’s family is Zwinglian, a Swiss denomination of Christianity.
Concerning Anglicans/Episcopalians, as I understand it, they’re pretty much one and the same. The term “Episcopal” started being used around the time of the American Revolution when for some reason things associated with England weren’t very popular.
I also happen to know how the American Methodist Episcopal church got started. A few years after the American Revolution, a black man named Absalom Jones lived in Philadephia. He was a very active member of his Episcopal Church and was responsible for bringing many black people to the Episcopal Church, slave and free alike. He also studied theology and took holy orders. Then came one Sunday morning when he sat down in his usual pew, only to be told that he, along with other black people, had to sit in the balcony, apart from the white members of the congregation. When he realized he would not be accepted as an equal in his own church, he asked the Bishop of Philadelphia if he could start his own church where black people would be equal. The bishop granted his permission, thus St. Thomas Church was founded for Americans of African descent. Today, the Episcopal Church recognizes him as a saint, and I see him as someone who should be emulated.
Guinastasia, they were Episcopalians all right. One day I mentioned something about going to a church get-together to a co-worker and she said, “Oh. Bingo?” I replied, “No, no, no. These are Episcopalians – wine and cheese!” 
CJ
According to ouisey, a Fundamentalist Baptist considers the following to be non-Christian:[ul]
[li]Latter Day Saints[/li][li]Jehovah’s Witnesses[/li][li]Unitarians[/li][/ul] but the first two defintely consider themselves to be Christian. Unitarians don’t.
Originally, Unitarians were heretics who rejected the doctrine of the Trinity. The trinity is one of the tenets of the Nicene Crede - ratified by the church in CE 325, but Unitarian congregations were first established in the 16th century (in Transylvania).
Universalists believe that no one will be condemned to damnation. Some might believe in a temporary separation from G_d, until the soul is ready to enter paradise. Universalism developed in America, about 1770.
The two merged into the Unitarian-Universalists (just say UU) in 1961. UU history
UU’s don’t have any set dogma. We believe in the “free and responsible search for truth and meaning” which means that each individual can decide what works for him/her. There are Buddhist UUs, Wiccan UUs, and atheist UUs - often in the same congregation. There are Christian UUs also, but they’re rare.
More info available here:UU FAQ
I’ve been aware of all of this since childhood - except the “October 31” part.
Now I’ve got a disconcerting mental picture of Martin Luther walking up to the door of the cathedral and calling out “Trick or Treat!” then nailing his theses to the door when the bishop didn’t give him any candy.
[sub]Well, that’s how it should have happened![/sub]
And while you’re at it, the Methodists, most of the Presbyterians, and a number of other groups in Canada all merged together to produce the United Church of Canada, the largest Protestant denomination in this country.
There’s also a St. Francis National Evengelical Spiritual Baptist Faith Archdiocese of Toronto just up the street. They sounded Pentecostal whenever I’ve passed the church (meaning they were very, very loud).
I’ve heard of Zwingli, but I didn’t know that there was still a separate Zwinglian church.
The Pentecostal movement started at the end of the 19th century-beginning of the 20th, I think. It was originally based on the revivification of the gift of speaking in tongues, which is mentioned several times in the Bible. Tongues can either mean speaking in a language you don’t know for the edification of someone who does speak that language, or speaking directly to God in a language nobody but He understands, and that’s connected to a few verses about “intercession in groans words cannot express”.
Man, I have got to figure out how to turn this into a pick-up line.
I was baptized Methodist when I was twelve and still call myself Methodist. I love the liberal bent and I feel 100% at home in their pews. (Never mind that I haven’t been in over a year.)
It was only a few years ago that I found out that Methodism comes out of the Anglican (Church of England) side instead of the Lutheran side… So my particular brand of Christianity comes from the lecherous King o’ England side. Extra bonus.
“Hey baby, ya wanna go ‘speak in tongues’?”
OH man, that double entendres in THAT one…
Really, JC, if ever there has been a time to use ;j …
I grew up in a small Southern-Baptist-dominated town, and it was my observation that they reproduce by fission. After a few years of association, petty little feuds tend to develop in the congregation. Eventually, one of the feuds gets big enough to polarize the group, and everyone starts looking for a doctrinal excuse to be mad at the other side. Polarization often happens along generational lines. Eventually, it reaches the point at which the only way to keep the peace is for one group to leave…and start another “First Baptist Church…”.
The process seems to take longer and be less likely in larger congregations, so this may be primarily a small-town phenomenon. Nevertheless, it’s possible that some splits originated as a result of purely personal animosity.
Calvinist checking in.
There are several denominations that consider themselves to be of the John Calvin school of thought: Presbyterian, Reformed, Ducth Reformed, Christian Reformed.
I’m Christian Reformed, a fairly conservative lot-- not as conservative as the Dutch Reformed, not as liberal as the Reformed. We sing hymns, women don’t wear anything on their heads, people often dress somewhat casually-- especially at the evening service. Basically, we’ve come a long way since Calvin first laid out his thoughts and plans. A lot of the tenets remain, but ol’ Calvin would probably roll over in his grave if he knew there were musical instruments and singing present in “his” churches.
For what it’s worth, among my friends, I’m given a hard time because I’m so “conservative” and “religious.” Among my family, I’m given a hard time because I’m so “liberal” and “don’t go to church enough.” Us modern-day Calvinists just can’t win.
Happy
Well, a lot of others have posted specific reasons that one denomination/sect/school of faith split or merged with another. Polycarp has, as usual, offered a very detailed set of links and a great history of specific doctrinal questions that separated various groups.
I think there may still be room for a 2-minute summary for JC And how ironic is that user name abbreviation in this context?
If one were to graph out the “lines of descent” for Christian denominations, they would resemble the family of some European royal family. For instance, both the Eastern Orthodox patriarchs and Roman Catholic pope consider themselves to have directly inherited the mantle of Peter and the true leadership of Christianity. The number of splits greatly exceeds the number of mergers, which are also numerous and greatly complicate the issue. Imagine this: Groups B and C historically both split from ancestral Group A. After some time, a large portion of Group C decides that the differences with Group B can be worked out and moves to merge the two groups. Some other portion of Group C refuses to go along and joins back to Group A, while another portion of Group B doesn’t want anything to do with those Group C heretics and forms Group D. Imagine that going on for over two thousand years and you arrive at the present situation.
What are they arguing about? Well, some of the doctrinal questions are truly basic questions of faith, such as salvation through faith versus salvation through works. Some others are truly the personality conflicts of the type Balance describes. Others are somewhere in between, such as some of the splits that have occurred in the various Anabaptist groups. It matters to the parties involved because they are debating the cost of eternal life, which are pretty high stakes. No matter how confusing and “petty” it may appear to an outsider.
Some of these denominations are pretty tolerant of the others, some are tolerant of only certain others, and some are convinced that everyone else is going straight to Hell. If you want a (over-)generalized rule of thumb, the more “conservative” or “righteous” a group claims itself to be, the less tolerant it tends to be.