It's no good to try and categorize Christian denominations into 3 neat categories, some may be conservative theologically, but liberal socially or morally, or vice versa.
anyway, the main branches of Christianity worldwide are:
[Roman or Vatican] Catholic churches. Among the oldest churches in christendom, headed by the Bishop of Rome, known as the Pope, or father. a variety of different national churches with various cardinals and patriarchs as their leaders, all united as one worldwide body. the structure is essentially episcopal, that is, with bishops, presbyters, and deacons, although other offices, such as sub-deacon, canon, &c. do exist. conservative on essential doctrines such as the Trinity and the Incarnation, does hold some controversial and misunderstood doctrines. morally conservative, although views of individual members do vary.
[Eastern] Orthodox churches: not to be confused with [Oriental] Orthodox Churches or the Church of the East. some orthodox Churches date from the time of the Apostles. national churches organisationally headed by bishops known variously as patriarchs, popes, metropolitans, or archbishops, are united by a common faith and common liturgy. most are in communion with the patriarch of constantinople (new rome), although some are not. particularly national churches include the Russian Orthodox Church, the Greek Orthodox Church, the Antiochian Orthodox Church, the Orthodox Church of Jerusalem, and the Serbian Orthodox Church. doctrinally conservative on essential doctrines, although some teachings and practices (as with the Catholic Churches) may appear strange to western protestant Christians. morally very conservative, although may appear socially progressive to some evangelicals.
[Oriental] Orthodox Churches: the primary churches are the armenian orthodox church and the coptic orthodox church, although there are others. very ancient churches, split from the orthodox and catholic over issue of Christ having one or two natures. some are beginning to move towards further communion with other churches, and their doctrine on the Incarnation is essentially the same as the EO and the CC. very similar to EO.
Churches of the East ["Nestorian"]. these churches are perhaps the most misunderstood in all of Christendom, and are very ancient. some of them acknowledge Nestorius as a saint and doctor of the Church. the Assyrian Church of the East is moving towards closer communion with the Catholic Church. morally and theologically conservative, similar in practice to EO and OO.
Anglican/Episcopal Churches: vary very widely, from liberal to highly conservative. the Church of England is one of the oldest in Christendom, and have spread their faith to many other countries throughout the world. recent splits over both theological and moral issues have detracted from the previous unity displayed by this communion.
Old Catholic: Similar in many ways to the Episcopalian or Anglican Churches, some are very conservative, others are more liberal. episcopal structure, most split from the Catholic Church rather late in the picture, while maintaining most of her traditional teachings.
Note: these first 6 are what are often called "apostolic churches" because they maintain an episcopal succession back to the Apostles. while other churches may date back to the Apostles, they do not have this unbroken episcopal succesion (some Lutheran churches are the exception)
Lutheran/Evangelical Catholic Churches: Some of these Churches, such as the Scandinavian Churches, are very ancient, others have been founded in more recent times. Like the Episcopalians, they vary widely, although much more likely to be doctrinally and morally conservative.
Reformed/Presbyterian: Because of recent doctrinal changes by some Presbyterian Churches, the name Presbyterian no longer also implies reformed as it once did. established in countries such as scotland, the netherlands, and some other european countries. some of these churches are very ancient, although significantly restructured during the 16th & 17th centuries. traditionally doctrinally and morally conservative, although some, such as the PCUSA, are more flexible today.
Anabaptist (Mennonite, Amish, &c.): Dating from the 16th century, these churches were formed by people splitting from the mainline churches over issues such as infant baptism, church and state, &c. morally conservative and orthodox in essential doctrines, some attracted a bad name through what a few members did.
Congregational: These churches split from the mainline churches over the issue of church government, believing that each congregation should be independent. they were once morally and doctrinally conservative, but now vary widely.
Baptist: Some of these are also Reformed, while others are not. most today are morally conservative, and orthodox in the essential doctrines, though rejecting infant baptism. structure is essentially congregational. mostly derived from 16th century splits from other protestant churches.
Methodist: can also be Reformed, strong emphasis on internal work of the Spirit. formed in the 18th century through splits from Anglicanism. today, vary widely in moral and social values, although doctrinally orthodox.
Pentecostal: these churches emphasise the importance of being Spirit-filled, including the gifts of the Spirit that were seen in the first century. most were formed in the 19th and 20th century. most are orthodox in the core doctrines, although some hold to the "oneness" heresy. many are morally conservative, some are morally conservative but socially progressive, while others are more liberal.
Seventh-day adventists: believe that the last day of the week is the Sabbath, and that this law of God is still relevant to today. have other, often misunderstood or misrepresented beliefs about the coming of Christ and the state of the soul after death. formed in the 19th century. morally conservative, and orthodox in the core doctrines.
other churches exist who do not belong to any denomination or Christian tradition, preferring simply to be called "Churches of Christ", "Christian Churches," or non-denominational
other sects claiming to be Christian:
Jehovah's Witnesses: deny the full deity of Christ. morally conservative, but doctrinally unorthodox (in fact, heretical). formed in the late 19th & early 20th centuries.
Church of Jesus Christ of Latter Day Saints ("Mormons"): morally conservative, but doctrinally heretical. deny many core doctrines of Christianity. formed in the 19th century.
sorry if i've missed any major branches, it wasn't intentional. hope this helps you.
