Heresy:  The obstinate post-baptismal denial of some truth which must be believed with divine and catholic faith, or it is likewise an obstinate doubt concerning the same.  (Catechism of the Catholic Church, 2089)
any anti-Catholics accuse Catholics of worshipping Mary.  Of course, there is no basis for this because the Church explicity forbids the worship of anyone other than God.  However, back in the early Church, there was group who did in fact worship Mary; they were known as "Collyridians".  Their excessive Marian devotion developed into a full blown worship of the Holy Virgin.  The heresy lasted about 100 years, existing between 350 and 450 A.D.
The great opponent of the Collyridian sect was Epiphanius, bishop of Salamis and a close colleague of St. Jerome.  One of his most outstanding contributions in defeating the Collyridians was his apologetic Panarion (Medicine Box).  In his refutation, he addressed both extremes of Marian heresies: Collyridianism (the super-exhaltation of Mary) and Antidicomarianitism (an Arabian movement which demoted and debased Mary's importance).
The Collyridian sect was comprised of mostly women who combined Catholic and Pagan rituals and beliefs and fused them into a new religion – not unlike, it should be observed, many pseudo Catholic nuns who do the same today.  Epiphanius considered this blasphemous, writing
…certain women there in Arabia have introduced this absurd teaching from Thracia: how they offer up a sacrifice of bread rolls in the Name of the ever-Virgin Mary, and all partake of this bread.
Heresy floats outside of the boundaries of the true faith.  One extreme exaggerates a truth; the other extreme denies it.  In the case of Collyridianism, we see a perfect example of the former: where there should be a veneration and devotion to Mary, there is an adoration of her instead.
onatism is a heresy which denies the intrinsic efficacy of the sacraments by conditioning their power on the worthiness of the minister of the sacrament.  Hence, if a minister was in a state of mortal sin, the sacrament would not be valid.  The Catholic teaching, of course, does not tie the validity of a sacrament to the moral state of the minister.  A corrupt minister can still dispense a sacrament's grace.
Donatism, flourishing in the fourth century, was skillfully promoted by Donatus, the bishop of Carthage, and later opposed by St. Augustine.  It drew its popularity and power by pitting various regional ethnic groups against Roman imperialism which came to be associated with the Church in Rome.  Its main propagation came from the brutal persecution of Diocletian (ending in 305) which caused many Christians to either suffer martyrdom or abandon their faith.  Those who survived the persecution became infuriated with those who renounced Christ but were later readmitted into the Church's communion after they had confessed their sin.  This led to a sort of puritanical theology in regards to the sacraments.  In this climate and with Donatus' deft organizational and rhetorical abilities, he and his supporters were also able to paint a picture of Roman primacy as foreign intervention and suppression.  Church historian Frederick van der Meer observed:
Donatism was from its inception a popular movement poor in original ideas, but nevertheless full of people who were easily inflamed and drawing from its principle strength.
Donatism has certain parallels to Protestantism.  Luther and his aristorcratic backers attempted (and succeeded) in selling the idea that Rome was a "foreign power".  The Church's corruption during the Reformation along with Luther's just anger over it fuelled the Reformation just like the re-admission of apostates (rightly so however) caused the Donatist schism and heresy.
bionism found its roots in a Jewish Christian named "Ebion".  The influence of the heresy spread not because of him, however, but rather as a popular and broad movement among Jewish Christians.  The heresy began in the first century and the New Testament has many recorded teachings which oppose it.  It lasted until the fifth century.  Its principal errors were:
The necessity of circumcision of all Christians
Denial of the deity of Jesus, claiming instead that he was an angel or man
Rejection of most of the New Testament, especially the Epistles of Paul
There were essentially three kinds of Ebionites during New Testament times:
1)
Judaizers – which proposed a strict view of Gentile circumcision
2)
Nazarenes – which proposed that all Jewish Christians must be circumcised
3)
Gnostic Jews – which insisted on keeping the Law but also added pagan elements
The Book of Acts recounts Peter's revelation from God which abolished the necessity of the ceremonial precepts of the Law.  Up until that time, however, the Church viewed itself as a branch of Judaism, and therefore the Mosaic Law and all its ceremonial prescriptions still had to be fulfilled.  In Acts 10, however, Peter was instructed that such a requirement was no longer binding on any Christian – Jew or Gentile.  In Acts 15, the controversy came to a climax when the Judaizers were insisting that the Gentiles be circumcised according the Law of Moses.  As we learn in this chapter, their insistence was rejected by the Apostles at the first Ecumenical Council in Jerusalem.  In addition to the book of Acts, there are many other places in the New Testament where not only the strict view of circumcising Gentiles was rejected, but also the necessity of circumcising Jews (Cf. Galatians 2:11, 1 Corinthians 9:20-21, Colossians 2:13-17, Romans 6: 14-15, 7:1-6).  Today, there are Christian sects which still hold to some parts of the Mosaic ceremonial law, including Messianic Jews and Seventh Day Adventists.
n the Greek, iconoclasm means "image breaker".  This heresy, like its name suggests, has a paranoid fear and rejection of the use of images or icons in religion.  With the exception of High Church Anglicanism, most Protestant Churches have a heightened aversion to the use of sacred pictures or objects in their worship services, whose attitude they assumed, ironically enough, from Islam.  Other contemporary sects who can be considered iconoclasts include the Mormons and Jehovah's Witnesses.
Although present throughout the Church's history, the most infamous period of iconoclasm occurred in the eighth century.  Because of the Islamic incursion in North Africa and Asia minor during this period of history, Emperor Leo III and iconoclastic Eastern bishops sought to sanitize the Faith of images which were offensive to Muslim eyes.  In so doing, they believed that conversions to Christianity might be more likely.  Through the reigns of Leo III, Constantine V, and Leo IV, iconoclasm was ruthlessly enforced by the systematic destruction of icons, statues, and sacred images.  Not until the Second Nicaean Council in 787 A.D., some 60 years later, was the ancient Catholic tradition restored and a distinction made between adoration ("latria") and veneration ("dulia").  The Council re-affirmed the constant custom of venerating religious images and icons while at the same time renouncing "icon worship".  Biblical evidence for the Church's position can be found in these passages: Exodus 25:18-22, Exodus 28:33-34, Exodus 37:7-9, Numbers 21:8-9, 1 Kings 6:23-28 1 Kings 7:23-29, 2 Chronicles ch. 3-5.
n response to the Jesuits' greater stress of man's free will as represented by the writings of theologian Luis de Molina, Cornelius Otto Jansen, bishop of Ypres in France, completed his work entitled Augustinus which sought to re-affirm the efficacy of God's grace in human affairs.  After his death, his multi-volume work, Augustinus, was condemned by the Holy Office in 1641, and then again by Pope Urban VIII's encyclical In Eminenti in 1643.  Its principal errors included denying the necessity of free will, affirming the irresistablity of grace, and affirming that such grace was only for the "elect".  In short, this heresy was simply a repeat performance of the Reformers' errors.
Jansenism did not begin to challenge the Church until Jansen was dead, and it was more famous for its political dimensions than it was for its theological questions.  By practicing a rigorous moral lifestyle, the Jansenists began to gain momentum against the Jesuits until it reached the pinnacle of political powerplay between the Church and the State.  After French Cardinal Jules Mazarin was able to secure Pope Innocent X's condemnation of the heresy (Bull Cum Occasione, 1653), this only cemented the Jansenists resolve to continue the struggle.  By a series of pamphlets called the Provinciales, they were able to gain widespread support among the populous and the secular clergy.  King Louis XIV, anxious to squash a perceived Jansenism's challenge to royal power, sought to silence the group.  After a truce was negotiated by Pope Clement IX in 1667, tension remained for the next few decades until Pope Clement XI condemned the work of a prominent Jansenist, Pasquier Quesnel.  After the Bull Unigenitus Dei Filius was issued in 1713, and although the proponents of the heresy still refused to accept Rome's decision, the movement died out by the mid-1700s.
Because of the resistance of the Pope's authority by some of the French bishops, Jansenism, as all heresies frequently do, led many into accepting yet another heresy.  The refusal of Papal authority on the question resulted in the heresy of Gallicanism raising its ugly head.  Gallicanism proposed that the Pope is subject to ecumenical councils.  Gallicanism was dealt its final death blow in 1870 at the First Vatican Council which defined Papal Infallibility.
arcionism is derived from its architect, Marcion, who was a wealthy ship-owner and the son of a bishop.  The heresy attacked the Christian teaching of monotheism, God's inherent goodness throughout the ages, and the compatibility between the Law of the Old Testament and the Gospel of the New Testament.  While other heresies fomented within the Church, Marcionism, because of Marcion's personality and organizational skills, constructed itself as a full-fledged schismatic body.
Marcion believed that there were two Gods.  The God of the Old Testament was cruel and vengeful while the New Testament God was loving and merciful.  He believed that the God who created the world was therefore tyrannical.  As his dualistic heresy spread, he was called before the Church at Rome in 144 and summarily excommunicated, even though his heresy survived in some forms for the next three centuries.
Marcion was a true heretic insofar as he picked and chose which books of the Bible he accepted as canonical.  Since he rejected Judaism completely, he ended up purging all of the Old Testament and most of the New Testament from his canon!  He kept the Pauline letters and most of the Gospel of St. Luke.
Some other his heresies included:
Rejection of the Resurrection
Denial of the Incarnation
Rejection of the Second Coming
Rejection of Marriage
Marcion was opposed by some of the greatest giants of Christian orthodoxy, including Justin Martyr, Irenaeus, Hippolytus, and Tertullian.  Their treatises, especially Tertullian's Against Marcion, spawned some of the greatest defenses of Christianity teachings on monotheism, the Trinity, and the holiness of marriage.
Marcionism also had an influence on Martin Luther.  As Marcion held to the incompatability of the Law and the Gospel, Luther did as well.  Current battles within Evangelicalism over the necessity to keep the Old Testament's moral law is also a leftover from Marcion's heresy.