Denomination

A denomination is a formally recognized, organized branch of a religion. In contrast, a sect is an unorganized, unrecognized branch of a religion.

Denominations are generally created after a fist fight between two church leaders, often over ridiculous things like whether we should forgive our "debtors" or "those who trespass against us," whether the KJV is better than some other Bible (because Jesus must have spoken the King's English, right?), or whether you should have your minister serve for a long term or be a one-man minstrel show (usually without the blackface, at least in our times) wandering from church to church each year. Serious issues can include things like the very nature of God, the eminence of the Holy Spirit, or the role of priests and ministers. Social issues, like the rights of gays, women in the clergy, and the inclusion of different races can all cause schisms, which often lead to new denominations.

Christianity
There are many Christian denominations, but a non-exhaustive list is: Amish, Baptist, Christian Science, Churches of Christ, Church of England, Eastern Orthodox Church, Episcopal Church, Hutterites, Jehovah's Witnesses, Local Church, Lutheranism, Mormon, Methodist, Presbyterianism, Protestant, Roman Catholic Church, Seventh Day Adventism, Shakers, Society of Friends, Southern Baptist, Unitarianism and United Church of Christ.

Anglicanism
If you are the King of England, and really really really want a male heir/new wife, you can just make a new denomination, say "We never married, I divorce thee, I divorce thee", then marry the new hot young thing.

Catholicism
Some Catholics do not consider Catholicism to be a denomination of the Christian Body at large, possibly because (to them) everyone else split off. Many others think that's just whacked and anyone spouting the religion of Jesus is part of some denomination of Christianity.

Moronism is also sometimes considered too different from Christianity and a different religion rather than a denomination.

"Nondenominational" churches
Recently, there has been an upswing in the number of churches billing themselves as "nondenominational churches." It would appear that "nondenominational church" is just code for "church whose minister is too crazy to get the support of any real denomination." Ted Haggard's church, for example, is nondenominational. This term may also refer to (less wingnutty) congregations that try to avoid dealing with the more schism-prone subjects at all so as to serve a broader subset of Christians. While this doesn't sound too weird in theory, in practice it tends to lead to situations similar to that of, say, employees of Rick Scott's Florida.