In school, I learned that the different gospels did copy a lot from each other. This was the explanation for why there are so many overlapping events between the gospels.
Is there substantial evidence to support this besides the bible?
Yes, although not quite the way you put it.
It is agreed by pretty much all Bible scholars that there is some degree of interdependence between the gospels. This is based on the fact that many of the stories in the gospels are told in a very similar way. Exactly what depended on what is the subject of much debate, and more information can be found on Wikipedia and Catholic Answers. This belief is very old, with Augustine laying down one of the most widely believed dependencies.
Some of the beliefs of dependency include:
It's worth pointing out that the interdependency has never been seen as in any way invalidating the gospels as sources. Any thorough modern biographer would also make use of other documents about their subject, and the parallel passages can be seen as evidence of the thoroughness and accuracy of the gospel writers. it's worth noting that all the gospels also contain some material found in no other gospel. Clearly none of the gospels was composed simply by copying other gospels. The wording differences are great enough to rule that out. Nor does it rule out the idea that the writers were eyewitnesses of at least some of the events themselves.
In answer to your final point, the only evidence for this is from analysis of the gospels themselves, though that includes the dating of manuscripts of the gospels and fragments of the gospels. None of the hypothesised sources such as Q has been definitively identified.
DJClayworth's answer is spot on. I'd like to take a moment to defend Bible scholars, their theories, and the gospel writers.
There is a serious question about whether John knew about the Synoptics. The Fourth Gospel was almost certainly the last written and it would seem the others would be available. But there's no textual evidence that I'm aware of that would show it copied from the Synoptics. Almost everyone who has ever considered the question views John as an independent source.
Luke explains in his prologue the methods he used to collect his sources:
Inasmuch as many have undertaken to compile a narrative of the things that have been accomplished among us, just as those who from the beginning were eyewitnesses and ministers of the word have delivered them to us, it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, that you may have certainty concerning the things you have been taught.—Luke 1:1-4 (ESV)
The translators of the NET Bible note on the word "narrative":
This is sometimes translated “narrative,” but the term itself can refer to an oral or written account. It is the verb “undertaken” which suggests a written account, since it literally is “to set one’s hand” to something (BDAG 386 s.v. ἐπιχειρέω). “Narrative” is too specific, denoting a particular genre of work for the accounts that existed in the earlier tradition. Not all of that material would have been narrative.
But what is clear from Luke's introduction is that he was aware of other compiled sources in addition to eyewitness testimony. Luke's expressed purpose is "to write an orderly account" so that Theophilus "may have certainty concerning the things [he has] been taught." He doesn't claim to be an eyewitness, but to have followed (some translations say "investigated") them. His approach is that of an ancient historian who takes a hodgepodge of sources (including his own eyewitness in the second volume, Acts) and compile them into a readable story for his patron. There was, in those days, no quotation mark, no footnotes, no concept of plagiarism, and no expectation that sources would be identified. By the ancient standards, Luke went above and beyond to write a convincing history of Jesus' life and of the early years of the Church.
One of the great discoveries of source criticism is that Luke and Matthew usually quote Mark when writing about material common to all three. To illustrate, here's the calling of Levi (AKA Matthew) with identical wording bolded and changed words italicized:
Mark 2:14 (NASB):
As He passed by, He saw Levi the son of Alphaeus sitting in the tax booth, and He said to him, “Follow Me!” And he got up and followed Him.
Matthew 9:9 (NASB):
As Jesus went on from there, He saw a man called Matthew, sitting in the tax collector’s booth; and He said to him, “Follow Me!” And he got up and followed Him.
Luke 5:27 (NASB):
After that He went out and noticed a tax collector named Levi sitting in the tax booth, and He said to him, “Follow Me.”
One parallel doesn't make the case, but over and over we see the pattern of Luke and Matthew editing Mark's material separately. Matthew wanted to use the name "Matthew" instead of Levi while Luke would like to clarify that the person in the tax booth was, in fact, a tax collector. These are reasonable edits and help the intended readers to understand the situation better. And again, by that era's standards, edited quotations without attribution was to be expected.
Not all the material in Luke and Matthew was copied from Mark. There is a substantial body of material that seem to be common to both. Careful examination of the passages common to Luke and Matthew suggest that each redacted (i.e. edited) another source. A wide variety of Biblical scholars have concluded that there was a written source (now lost) that consisted mostly of Jesus' teachings that both Matthew and Luke independently drew from. This hypothetical document was called Quelle (German for "source") by its early proponents and is now simply called Q.
Some scholars dispute the existence of Q and others say that it was likely an oral, not written, source. Given that one of the primary duties of a Rabbi's disciples in that period was to memorize the teacher's words, the Q material may very well represent our Lord's teachings as a Rabbi. But none of these theories is supported by external evidence and so must be held loosely.
Other material, particularly related to Jesus' birth, is unique to Matthew and Luke respectively.
Doesn't it harm our faith to accept that the gospels copied each other? I can imagine some thinking.
Remarkably, the Passion narrative of each gospel is independent. Fully one third of Mark (and a similar proportion of the other three gospels) is absolutely unique to it. That means that for the most critical week of our Savior's life, we have four independent accounts. What's more, while they do disagree on some details (the classical example is who was at the tomb), they all agree that Jesus died and bodily rose again1. Further, they agree on why these events happened.
Christian ought to rejoice in the care that Matthew and Luke took when writing down their biographies of Jesus. Both used independent sources when available and diligently edited Mark's accounts when necessary. We can take comfort in knowing that the gospel writers were eager to leave us with complete and accurate narratives of Jesus' life. We should rejoice in the blessing of Christ's story handed down to us from the testimony of many witnesses.
The Synoptic gospels do copy each other and that should be encouraging to Christians.
Mark's ending is a tricky problem in textual criticism. It seems to end in mid-sentence after Mark 16:8. The ESV translators note:
16:9 Some manuscripts end the book with 16:8; others include verses 9–20 immediately after verse 8. At least one manuscript inserts additional material after verse 14; some manuscripts include after verse 8 the following: But they reported briefly to Peter and those with him all that they had been told. And after this, Jesus himself sent out by means of them, from east to west, the sacred and imperishable proclamation of eternal salvation. These manuscripts then continue with verses 9–20
Exactly what happened at the end of the gospel is not clear, but many (including N. T. Wright in The Resurrection of the Son of God) believe that the original autograph was damaged and we lost the final portion of the gospel. The various endings according to this view are attempts to reconstruct the text using fragments of Luke and plausible guesses. But we should not consider any of these endings as authentic as they all differ in style and theme from Markian material. Thankfully, we do have enough of the ending to assert that Jesus rose from the dead and that the tomb was empty:
And he said to them, “Do not be alarmed. You seek Jesus of Nazareth, who was crucified. He has risen; he is not here. See the place where they laid him.—Mark 16:6 (ESV)
What we are missing here is any post-resurrection appearances. This deficiency is amply corrected by the other gospels and by Paul in 1st Corinthians 15.
I'd generally agree with Clayworth, but let me add a couple of points.
The evidence is purely from textual analysis: There are large sections of Mark that also appear in both Matthew and Luke, and there are things in both Matthew and Luke not found in Mark.
The similarities aren't as blatant as some imply. It's arguable that the similarities are because the writers are describing the same events, and not because they copied from each other. But I'd agree that this is unlikely. There are too many similarities, including identical wording in some places. One or two such cases could be coincidence, but there are hundreds.
I'm a little surprised the Clayworth doesn't mention what I thought was the most popular theory: That Mark was written first, and Matthew and Luke used Mark as a source. Then that there was another source which no longer exists today, called "Q" (from the German word "quellen" meaning source) that Matthew and Luke also used.
Q is mostly quotes from Jesus: sayings, slogans and sermons. So Q may have been a collection of "sermon notes".
Papias, an early church historian, mentions that Matthew compiled a collection of quotes from Jesus that he called "The Sayings", written in Aramaic. I wonder if this book by Matthew could be the mysterious "Q". I understand that language scholars say that the Q quotes in Matthew and Luke appear to be translated to Greek from Aramaic based on wording and grammar. (I am not a linguist so I can't evaluate this.) But as far as I know there's no further evidence for or against.
I'm always a little amused when I hear this analysis used as an argument against the authenticity of the Gospels. I've heard some critics discuss the parallels it as if they were some great secret revelation that Christians are unaware of or are trying to hide. But any study Bible I've ever owned has a section called "Gospel Parallels" or "Harmony of the Gospels" or some such that lists these parallels verse by verse. And as others have indicated, in any other subject, studying the work of those who have come before you is called "research" and "scholarship". But when it comes to the Gospels suddenly it becomes "cheating" or "deceit" or something. (Yes yes, if the Gospel writers did copy from each other, they failed to include proper footnotes. Maybe because the MLA handbook wasn't written until 2000 years later.)
The fact that some people are taught in school that the gospel writers copied from each certainly does not make it so. One question that arises at the outset is, "Why would the gospel writers copy from each other?
If, the gospel writers were each eyewitnesses, then there would be no need to copy from each other, since each would be recalling events from personal experience. However, if the gospel writers were not eyewitnesses, then the need for copying becomes apparent.
There is sufficient evidence to support the idea that the authors were, indeed, eyewitnesses, though this should be covered in a separate question and is certainly disputed by some.
Another question that arises is, if the gospel writers were copying from each other (or a different source), what was the purpose of even creating very similar accounts of the same story? Why not just stick with the original source? It doesn't seem to make much sense. It only makes sense if the original source was not a written "Q" document, but the actual eyewitness experiences of the three authors.
A great question to ask is, "What would we expect to find if the gospel writers did, in fact, copy from each other?" We would expect to find very significant agreement in the details of each event as well as the order. However, we find quite a few differences. Luke includes details about John the Baptist and Elizabeth, while the others do not. Matthew introduces us to the Magi, while the others do not. Matthew's genealogy does not match Luke's, and Mark leaves it out altogether. The text of the Sermon on the Mount differs significantly between Luke and Matthew, and Mark again omits it. The three differ on the specific details given about the trial, death, and resurrection of Christ.
Copying from each other does not seem to be able to account for so many differences. It is much more sensible to conclude that each recorded what impressed them most from their shared experiences of the same events.
Now, there are a lot of the same events mentioned in each of the Synoptics. It is reasonable to assume that each is confirming the accounts of the others by giving their own accounts of many of the same events. Each wrote for a specific purpose for a specific audience. It is certainly likely that the second and third authors were aware of those that wrote before them, and this could have shaped the event selected in their own writings.
So, we can't know with absolute certainty, but it is certainly rational and reasonable to conclude that each author shared his own record of events, highlighting what impressed him the most.