For easy reference with the heretic post (and cuz I'm bored)

(all are copy pasted from wikipedia, as per the GNU Free Documentation Liscensing)

Modalism

In Christianity, Sabellianism (also known as modalism) is the third-century belief that the three persons of the Trinity are merely different modes or aspects of God, rather than three distinct persons. It is attributed to Sabellius, who taught a form of this doctrine in Rome in the third century. Hippolytus knew Sabellius personally and mentioned him in the Philosophumena. He knew Sabellius disliked Trinitarian theology, yet he called Modal Monarchism the heresy of Noetos, not that of Sabellius. Sabellianism was embraced by Christians in Cyrenaica, to whom Demetrius, Patriarch of Alexandria, wrote letters arguing against this belief.
The chief opponent of Sabellianism was Tertullian, who labelled the movement "Patripassianism", from the Latin words patris for "father", and passus for "to suffer" because it implied that the Father suffered on the Cross. It was Coined by Tertullian in his work Adversus Praxeas, Chapter II, "By this Praxeas did a twofold service for the devil at Rome: he drove away prophecy, and he brought in heresy; he put to flight the Paraclete, and he crucified the Father." It is important to note that our only sources extant for our understanding of Sabellianism is from their detractors. Scholars today are not in agreement as to what exactly Sabellius or Praxeus taught.
Today, Sabellianism is rejected by most types of Christianity and some argue that it logically leads to Nestorianism. It is accepted primarily by some Pentecostal groups, sometimes referred to as Oneness Pentecostals or "Jesus Only" Pentecostals.
Historic Sabellianism taught that God the Father was the only person of the Godhead. This teaching proports that the identity of God the Father and Jesus is the same. According to this belief, the terms "Father" and "Holy Spirit" both describe the one God who dwelt in Jesus. Some Oneness detractors call this the "Jesus-Only doctrine".

Peleganism

Pelagianism is a belief that original sin did not taint human nature (which, being created from God, was divine), and that mortal will is still capable of choosing good or evil without Divine aid. Thus, Adam's sin was "to set a bad example" for his progeny, but his actions did not have the other consequences imputed to Original Sin. Pelagianism views the role of Jesus as "setting a good example" for the rest of us (thus counteracting Adam's bad example). In short, humanity has full control, and thus full responsibility, for its own salvation in addition to full responsibility for every sin (the latter insisted upon by both proponents and opponents of Pelagianism).
Pelagianism was opposed by Augustine of Hippo, leading to its condemnation as a heresy at several local synods. These condemnations were summarily ratified at the Council of Ephesus, although it was not considered a major act of that council.
Pelagianism never vanished completely from Christian history; it survived in variations like Semi-Pelagianism, which was born during the 19th century evangelical American revival movement and by its defenders, with the theology espoused by Charles Finney.

Monophysitism/Apollinarian

Monophysitism (from the Greek monos meaning 'one, alone' and physis meaning 'nature') is the christological position that Christ has only one nature, as opposed to the Chalcedonian position which holds that Christ has two natures, one divine and one human. There are two major doctrines that can undisputedly be called monophysite:
Eutychianism holds that the human nature of Christ was essentially obliterated by the Divine, "dissolved like a drop of honey in the sea".
Apollinarianism holds that Christ had a human body and human "living principle" but that the Divine Logos had taken the place of the nous, or "thinking principle", analogous but not identical to what might be called a mind in the present day.
The radical monophysitism of Eutyches emerged in Egypt as a response to Nestorianism. It was rejected at the Council of Chalcedon in 451 and is also rejected by the Oriental Orthodox Churches.
Later, monothelitism was developed as an attempt to bridge the gap between the monophysite and the Chalcedonian position, but it too was rejected by the Chalcedonians, despite at times having the support of the Byzantine Emperors. Some are of the opinion that monothelitism was at one time held by the Maronites, but they, for the most part, dispute this, stating that the Maronite Community has never been out of communion with the Roman Catholic Church.
Miaphysitism, the Christology of the Oriental Orthodox Churches, is sometimes considered a variant of monophysitism, but these Churches take pains to distinguish their teaching from monophysitism per se.

Nestorianism

Nestorianism is the Christian doctrine that Jesus existed as two persons, the man Jesus and the divine Son of God, rather than as a unified person. This doctrine is identified with Nestorius (c.386–c.451), Patriarch of Constantinople, although it is inappropriately named since he himself denied holding this belief. This view of Christ was condemned at the Council of Ephesus in 431, and the conflict over this view led to the Nestorian schism, separating the Assyrian Church of the East from the Byzantine Church.
Historical references to Nestorians are to the Assyrian Church of the East, commonly described as Nestorian because it refused to drop support for Nestorius and denounce him as an heretic. However the church of the east does not teach Nestorianism, but rather teaches the view of Babai the Great, that Christ has two qnome (essences) which are unmingled and eternally united in one parsopa (personality). The origin of this confusion is mostly historical and linguistic: for example, the Greeks had two words for 'person', which translated poorly into Syriac, and the meaning of these terms were not even quite settled during Nestorius's lifetime.
Nestorianism as a Christological heresy originated in the Church in the 5th century out of an attempt to rationally explain and understand the incarnation of the divine Logos, the Second Person of the Holy Trinity as the man Jesus Christ. Nestorianism teaches that the human and divine essences of Christ are separate and that there are two persons, the man Jesus Christ and the divine Logos, which dwelt in the man. Thus, Nestorians reject such terminology as "God suffered" or "God was crucified", because they believe that the man Jesus Christ suffered. Likewise, they reject the term Theotokos (Giver of birth to God) for the Virgin Mary, using instead the term Christotokos (Giver of birth to Christ) or Anthropotokos (Giver of birth to a man).

Monarchism

Monarchianism, or Monarchism as it is sometimes called, is a set of beliefs that emphasize God as being one, that God is the single and only ruler.
This emphasis conflicted with the doctrine of the Trinity, of God as Father, Son, and Holy Spirit. Models of resolving the tension between the two principles in favour of God's oneness were proposed in the 2nd century, but rejected as heretical by the Church.

Gnosticism

(wikipedia entry gives far too much detail)

Adoptionism

Adoptionism is a view held by some early medieval Christians, that Jesus was born a human only, and was not divine until his baptism, at which point he was adopted as the Son by God the Father.

Donatism

Their primary disagreement with the rest of the Church was over the treatment of those who forsook their faith during the Persecution (303–305 AD) of Diocletian. The rest of the Church was far more forgiving of these people than the Donatists were. They refused to accept the sacraments and spiritual authority of the priests and bishops who had fallen away from the faith during the persecution. Many church leaders had gone as far as turning in Christians to the Roman authorities and had handed over sacred religious texts to authorities to be publicly burned. These people were called traditors ("people who had handed over"). These traditors had returned to positions of authority under Constantine, and the Donatists proclaimed that any sacraments celebrated by these priests and bishops were invalid. As a result, many towns were divided between Donatist and non-Donatist congregations. The sect had particularly developed and grown in North Africa. Constantine, as emperor, began to get involved in the dispute, and in 314 he called a council at Arles in France; the issue was debated and the decision went against the Donatists. The Donatists refused to accept the decision of the council, their distaste for bishops who had collaborated with Rome came out of their broader view of the Roman empire. After the Constantinian shift when other Christians accepted the emperor as a leader in the church, the Donatists continued to see the emperor as the devil. In particular, the birth of the Donatist movement came out of opposition to the appointment of Caecilian as bishop of Carthage in 312 AD because of his pro-government stance. In 317 Constantine sent troops to deal with the Donatists in Carthage, for the first time Christian persecuting Christian. It resulted in banishments and even executions. It failed completely and Constantine had to withdraw and cancel the persecutions in 321.
Donatists were more than just an opposition movement. They also had a distinctive worship style, emphasizing ‘mystical union of the righteous inspired by the Holy Spirit and instructed by the Bible.1 Anabaptists and other radical church traditions have looked to Donatists as historical predecessors because of their opposition to the union of state and church, their emphasis on discipleship and, in some cases, their commitment to nonviolence and social justice. Like those in the Radical Reformation in the 16th century, the Donatists saw the Catholics as impure and corrupted.

Socinianism

Socinianism summarises the beliefs of the Socinians, followers of Laelius Socinus (died 1562 in Zürich) and of his nephew Faustus Socinus (died 1604 in Poland).
The Socinians congregated especially in the Transylvania, in Poland (see Polish brethren) and in the Netherlands. They held sceptical views on reason and rejected orthodox teachings on the Trinity and on the divinity of Jesus, as summarised in the Racovian Catechism.

Albigensians

Albigensians (French: Albigeois) literally means the inhabitants of Albi, a city in southern France. However, the term was used to refer to the followers of Catharism, a Gnostic-like religious movement of southern France in the 12th and 13th century. The name originates from the end of the 12th century, and was used in 1181 by the chronicler Geoffroy du Breuil of Vigeois. The name is somewhat misleading as the center of the religious movement was really Toulouse.
They believed that the principles of good and evil continually oppose each other in the world. The Albigenses opposed marriage, bearing children (because they thought bringing life into the world to be a sin), and eating meat. They advocated suicide, especially by starvation (so that when they died, they would have little taint on them and free of Earthly desires). In the 14th century the church declared them heretics. In the years that followed the Crusades and Inquisitions against them, they slowly disolved, and by the 15th century they had completely disappeared.

Arianism

Arianism was a Christological view held by followers of Arius, a Christian priest who lived and taught in Alexandria, Egypt, in the early 4th century. Arius taught that God the Father and the Son were not co-eternal, seeing the pre-incarnate Jesus as a divine being but nonetheless created by (and consequently inferior to) the Father at some point, before which the Son did not exist. In English-language works, it is sometimes said that Arians believe that Jesus is or was a "creature"; in this context, the word is being used in its original sense of "created being."

Docetism

In Christianity, Docetism is the belief, regarded by most theologians as heretical, that Jesus did not have a physical body; rather, that his body was an illusion, as was his crucifixion.
This belief is most commonly attributed to the Gnostics, who believed that matter was evil, and hence that God would not take on a material body. This sort of statement, however, is rooted in the idea that a divine spark is imprisoned within the material body and that the material body is in itself an obstacle, deliberately created by an evil lesser god (the demiurge) for this purpose, that prevents man from seeing his divine origin. Humanity is, in essence, asleep.