What are the lost gospels of the New Testament?

One of the reasons these books aren't in the New Testament is because of their late date; therefore, they couldn't have been written by an apostle or one of their associates (i.e. apostolicity) and therefore aren't authoritative. As B.B. Warfield wrote:

The Canon of the New Testament was completed when the last authoritative book was given to any church by the apostles, and that was when John wrote the Apocalypse, about A.D. 98.

Another test these books fail is that they aren't consistent with those books we know belong in the canon; they aren't inspired by the Holy Spirit (2 Tim. 3:16-17; 2 Pet. 1:20-21). In addition, these books below weren't widely circulated amongst various early churches (i.e. catholicity). Lastly, as F.F. Bruce wrote:

By the time of Irenaeus, who, though a native of Asia Minor, was bishop of Lyons in Gaul about A.D. 180, the idea of a fourfold Gospel had become so axiomatic in the Church at large that he can refer to it as an established and recognized fact as obvious as the four cardinal points of the compass or the four winds:

For as there are four quarters of the world in which we live, and four universal winds, and as the Church is dispersed over all the earth, and the gospel is the pillar and base of the Church and the breath of life, so it is natural that it should have four pillars, breathing immortality from every quarter and kindling the life of men anew. Whence it is manifest that the Word, the architect of all things, who sits upon the cherubim and holds all things together, having been manifested to men, has given us the gospel in fourfold form, but held together by one Spirit.

The Nag Hammadi library (aka: the Gnostic Gospels) is a collection of thirteen ancient codices containing over fifty texts discovered near the Upper Egyptian town of Nag Hammadi in 1945. Gnosticism (from the Greek gnosis, meaning "knowledge") is said to have been the second great heresy faced by the early church (the first being the Judaizers). Gnosticism essentially observed, (1) salvation was a matter of acquiring and using secret knowledge, essentially self-knowledge; (2) it taught that Christ was lower than God, merely a pantheistic emanation; and (3) it denied the incarnation, etc. It influenced numerous cults and false teachers, and even today it is seen in such works as Dan Brown's The Da Vinci Code.

The chart below contains a list of a number of alleged "lost gospels" or "lost books" that are not and should not be in the New Testament.

App. Date A.D.	Book Name
225	Acts of John
185	Acts of Peter
190	Acts of Paul
150	Acts of Andrew
215	Acts of Thomas
150-250	Apocalypse of Peter
175-225	Apocryphon of James
150-225	Apocryphon of John
150-200	Dilogue of the Savior
300	Epistle to Laodiceans
Late 1st Cen.	Eugnostos the Blessed
175	Excerpta ex Theodoto
5th-6th Cen.	Gospel(s) of Bartholomew
16th Cen.	Gospel of Barnabas
150	Gospel of Ebionites
150	Gospel of Hebrews
2nd Cen.	Gospel of Judas
120-180	Gospel of Mary Magdalene
150	Gospel of Nazareans
150	Gospel of Nicodemus (Acts of Pilate)
150	Gospel of Peter
175-225	Gospel of Philip
2nd-3rd Cen.	Gospel of the Egyptians
2nd Cen.	Gospel of the Savior
90-180	Gospel of Thomas
225	Infancy Gospel of Thomas
200-250	Gospel of Thomas the Contender
150	Gospel of Truth
3rd Cen.	Hypostasis of the Archons
150-200	Interpretation of Knowledge
175-200	Letter to Rheginos (Treatise on the Resurrection)
150	Protoevangelium of James
2nd Cen.	Pistis Sophia
175-200	Second Treatise of the Great Seth
2nd Cen.	Sophia of Jesus Christ
275-325	Teachings of Silvanus
175-200	Treatise on the Resurrection (Letter to Rheginos)
3rd-4th Cen.	Tripartite Tractate
175-200	Valentinian Exposition

For a more complete study concerning the New Testament canon I would suggest reading the articles below.

References:

Bock, Darrell. The Missing Gospels: Unearthing the Truth behind Alternative Christianities (Nashville: Thomas Nelson, 2006).
Bruce, F.F. The New Testament Documents: Are They Reliable? (5th edition; Leicester: Intervarsity Press, 1959).
Warfield, B.B. The Canon of the New Testament: How and When Formed. (Philadelphia: The American Sunday-School Union, 1892).

Related Topics:

Apocrypha Accounts?
The Catholic Bible?
God's Flawless Word
What is heresy?
What is Gnosticism?
The Formation of the Canon of the New Testament
Introduction to the New Testament