To talk about all the individual denominations would take a long time, but there are a few broad categories that can be easily talked about.
Polity
One of the major differences between denominations is polity, or church government. There are three forms of church polity, I'll note which churches use which.
Episcopal - Rule by Bishops. Church leaders are called priests, and are appointed by higher ranking leaders called bishops, ultimately appointed by an archbishop. All church decisions are made top-down in an autocratic authority structure. Edit: Some churches, particularly African-American denominations, are Episcopal in polity but don't use the term "priest," instead using "pastor" or "reverend."
Presbyterian - Rule by Elders (Presbyter means "elder" in Greek). Church leaders are called Elders, pastors are elders with license to preach. Elders are elected by congregational vote, and church decisions are made by the session of elders, which includes the pastor and any ruling elders elected. Quarterly all the elders in a geographic area called a Presbytery meet to discuss and vote on matters of doctrine and practice, and yearly representatives from each Presbytery meet in a General Assembly for the same. No centralized leadership, moderators of the General assembly are elected per assembly.
Congregational - Rule by Congregation. Pastors are elected by congregational vote and all major church decisions are decided the same way. When churches are part of a denomination it's usually a more loose association without any authority exercised other than the ability to revoke membership of a church from that association. Often the de-facto leadership of congregational churches becomes autocratic when a pastor becomes powerful enough to influence all decisions to go his way.
Churches which are not Protestant:
- Roman Catholic (Episcopal polity)- Politically conservative on moral issues (abortion, sexuality, contraception), but liberal on social issues (matters of charity and collective responsibility to the underprivileged). The most tradition-bound church, with lots of traditions that were abandoned by most other churches after the Protestant Reformation. It's hard to generalize Catholics because there are so many of them, over a billion, so you'll find a lot that may resemble more traditionally politically conservative views (Rick Santorum), and others that are politically liberal (John Kerry).
- Various Orthodox (Episcopal polity)- Broke off from the Catholic Church in the 11th century over issues of autonomy and some theological issues. Similar in belief to Catholics, high emphasis on tradition and ritual, differences are mostly in some traditional practices and culture (it's a vastly different culture.) Unlike the Catholics they don't have one unifying figurehead leader like the Pope. They have a number of different Patriarchs that serve a similar role in their area of responsibility (Greece, Russia, etc.)
- Anglican/Episcopal (sort of) (Episcopal polity)- Protestant churches are technically those formed as a result of the Protestant Reformation started by Martin Luther. The Anglican church split off from the Catholic church in tandem with, but separate from, that reformation, however it aligned itself with a lot of the beliefs of the Reformation by the time of Elizabeth I. The American and British branches are politically and theologically liberal. All other areas, particularly Africa and Southeast Asia are the polar opposite, and it's a big controversy in the Anglican Communion.
Protestant Churches:
Protestant Churches all trace their origin back to the protestant reformation of the 16th Century. It was kicked off by a priest named Martin Luther, who, after reading the Bible and comparing it to the teachings and practice of the Church (It wasn't called "Roman Catholic" yet), came to believe that there were a large number of inconsistencies and blatant heresies in those traditions and practices.
There is a lot of overlap in the following categories, many churches fall into two or three of these categories. Since I'm familiar with US denominations I'm going to use those as examples.
MAINLINE - Churches that fell on the "modernist" side of the 1920's fundamentalist/modernist controversy. Called mainline because most people who were in these denominations stayed in them when the fundamentalists left. Tend to be theologically and politically liberal (Support gay marriage and abortion rights). Examples:
- United Methodist Church (Episcopal polity)
- Presbyterian Church (USA) (Presbyterian polity)
- Evangelical Lutheran Church in America (Episcopal polity)
- United Church of Christ (Congregational Polity)
- Episcopal Church in America (Episcopal polity)
EVANGELICAL - Churches which stress the importance of personal conversion, evangelism, and Biblical inerrancy. Are theologically conservative. Tend to be politically conservative (opposed to gay marriage and abortion). Examples:
- Southern Baptist Convention (and most other baptists) (Congregational polity) - These are the most "stereotypical" evangelicals. They get their name because they don't baptize infants, unlike all the other denominations mentioned so far. Most Independent or "non-denominational" churches are Baptist in theology and practice, often with Charismatic elements added.
- Lutheran Church - Missouri Synod (Congregational Polity)
- Most Reformed Churches
- Most Independent or "non-denominational" churches
- Most Charismatic Churches
REFORMED - Churches which adhere to the doctrinal principles of John Calvin and usually conform themselves to one of the Reformed Confessions (The Westminster Confession of Faith, The London Baptist Confession, The Three Forms of Unity). The most uniformly theologically conservative group. Tend also to be overwhelmingly politically conservative. Are all Presbyterian in polity except for the Reformed Baptists and any which describe themselves as non-denominational like Acts 29 churches often do. Edit: Reformed Baptists and Independent Reformed churches often practice a modified form of Presbyterian polity where they elect elders who have group authority, but don't report to a local presbytery the way traditional Presbyterian churches do. Examples:
- Presbyterian Church in America
- Orthodox Presbyterian Church
- Associate Reformed Presbyterian Church
- United Reformed Churches in North America
- Most "Acts 29" churches
- Reformed Baptists within the Southern Baptist convention and other baptist denominations.
CHARISMATIC/PENTECOSTAL - Churches which emphasize the work of the Holy Spirit through the spiritual gifts and miracles. Commonly characterized by "speaking in tongues" in public worship. Pentecostal churches tend to be much more culturally conservative, dressing differently and preaching "Holiness", which to them is being outwardly different from the rest of their culture in appearance and behavior. Examples:
- Assemblies of God (Congregational polity)
- United Pentecostal Church (Congregational polity)
- Vineyard Churches (Congregational polity)
- Church of God (Episcopal Polity)
- Calvary Chapel churches (Congregational polity)
- Many Independent or "non-denominational" churches.
ANABAPTIST - Churches whose members practice a radically different lifestyle than other modern Christians. They often form tight-knit rural communities set apart by archaic clothing, avoidance or elimination of the use of modern technology, and avoidance of interaction with the greater culture. They are all extremely pacifistic. All Anabaptist are Congregational. Examples:
- Amish
- Mennonites
- Hutterites
- Brethren
AFRICAN-AMERICAN DENOMINATIONS - Distinctive to the United States are denominations which are, intentionally or de facto, predominantly African-American. They often have a lot in common with more broadly evangelical churches and charismatic churches, with the notable exception of being much more political, and liberally political in particular, unlike other evangelical churches. African-American denominations tend to be much more involved in social justice and civil rights causes. Episcopal polity is much more common in African-American evangelical churches than it is in denominations which aren't distinctively African-American. If you've never heard of any of these denominations it's probably because you've never driven through, or interacted with people from, impoverished sections of major US Cities. Examples:
- African Methodist Episcopal (AME) (Episcopal polity)
- Christian Methodist Episcopal (CME) (Episcopal polity)
- Church of God in Christ (C.O.G.I.C.) (Episcopal polity)
- National Baptist Convention (Congregational polity)
- National Missionary Baptist Convention of America (Congregational polity)
"NON-DENOMINATIONAL" - I put this in quotes because it's a term that doesn't have a lot of truth to it. I think "Independent" would be a better term. "Non-denominational" churches still have particular beliefs which set them apart from other bodies of believers, and "denomination" simply means a separate group distinct from other groups. It is a strange conceit to think that since your particular distinct congregation or group of congregations doesn't label itself a denomination that somehow that's a praiseworthy attribute. Edit: Most independent churches are Congregational in polity. Sometimes, however, they can transform into or begin as a modified form of Episcopal government where the pastor has a Bishop-like autocratic authority, sometimes even being called Bishop. Most churches with charismatic (in personality, not theology), well known pastors are independent.
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