There are passages in the Gospels in which Jesus says that His current generation would not pass away before He returned in His kingdom, or that He was to return very shortly:
However, this did not come to pass during the lifetimes of the Apostles, or the generation of Jesus. The events spoken of in the Olivet Discourse did not happen, and Jesus did not return. This has led to various interpretations of Jesus's statement that "This generation shall not pass, till all these things be fulfilled", the most popular ones being:
In short, while certain explanations may seem sufficient to explain a passage on its own, it seems that none of the explanations which are commonly put forth can satisfy what is demanded when all of the passages are considered together, taking into account what Jesus's original audience would have been understanding Him to say.
Additionally, in the rest of the New Testament, the writers frequently speak of the fact that they believed that the kingdom was very shortly to come (Romans 13:11-12, 16:20: 1 Corinthians 7:29: Philippians 4:5, Hebrews 10:37, James 5:7-8: 1 Peter 4:7 Revelation 1:1, 1:3, 22:6). So, the belief amongst those who actually spoke to Jesus or his followers was that He was to return very soon, probably near the end of their lifetimes. Yet, it did not happen, and the resolutions which preserve the "correctness" of the prophecies in spite of that simply do not seem to work, contextually.
An alternative explanation - one that will forever be unpopular, because it maintains that something which Jesus spoke of did not happen in the timeframe in which He said it would happen - is that God delayed Jesus Christ's second coming. Jesus preached a very short timeframe for His coming, and yet, God delayed the event, because of reasons that He deemed important enough, such as what is suggested by 2 Peter 3:1-15 - that it allows more time for repentance, and gives more people an opportunity to be saved.
This view involves viewing Biblical prophecy as implicitly and inherently conditional, rather than necessarily setting something in stone (2 Samuel 12:13-23, Jeremiah 18:1-10, 26:3-6, 26:17-19, Joel 2:11-14, Jonah 3:4-10). The condition, in this case, is repentance, and God has on that basis (or others known to Himself) delayed something which was originally to happen, at least potentially, in the first century.
The Revised English Version (REV) takes this position in its lengthy commentaries on the passages in question, which contain the following excerpts:
Revised English Version - Matthew 16:28
In summary, it needs to be restated that the one and only reason that anyone says that the Transfiguration, resurrection, Day of Pentecost, or other events that occurred in apostolic times is what Christ was talking about in Matthew 16:28 is that the people he was speaking to are dead, which makes Christ's statement not historically accurate. But prophets and apostles such as Ezekiel, Isaiah, Joel, Zechariah, Peter, Paul, and John also wrote that the Day of the Lord was close at hand, and what they said has turned out to be inaccurate too. What we see is that God is a God of mercy, and for His own purposes He delays the timing of the End without announcing that He will do so, most likely in the hope that more people will get saved and join Him in Eternity. For his part, Jesus, like the prophets of old, could not go beyond what God revealed to him, and, in the case of the time of the Second Coming, God had indicated it was coming soon.
Revised English Version - Matthew 24:34
F. F. Bruce writes, "When we are faced with the problem of understanding a hard saying, it is always a safe procedure to ask, 'What would it have meant to the people who first heard it?' And there can be but one answer to this question in relation to the present hard saying. Jesus' hearers could have understood him to mean only that 'all these things' would take place within their generation. Not only does 'generation' in the phrase 'this generation' always mean the people alive at one particular time, the phrase itself always means 'the generation now living.' Jesus spoke of 'this generation' in this sense several times, and generally in no flattering terms."
In saying that, F. F. Bruce is correct. The simple and straightforward meaning of what Jesus said was that that generation, the generation that he and his disciples lived in, would not pass away until all the signs he spoke of were fulfilled. The only difficulty is that the generation died and the signs were not fulfilled; the Second Coming did not occur and the age did not end. But God has the authority to delay the Second Coming, and He did. Jesus only spoke what God revealed to him, and he also had very good scriptural reason to believe that the Tribulation would come very shortly after his death and resurrection, certainly within his generation.
Additionally, in the book When the Son of Man Didn't Come - A Constructive Proposal on the Delay of the Parousia, this position is developed and argued for:
When the Son of Man Didn't Come, edited by Christopher Hays - Chapter 3, pg. 57
At this stage, it is vital to emphasize the main point of this chapter: the biblical evidence indicates that in order to understand predictive prophecy, we need to read prophecy with a hermeneutic of activation, not one of prognostication. Because the eschatological proclamation attributed to Jesus is predictive prophecy, it requires this approach too. The intent of Jesus' public declarations was not simply to provide foreknowledge of the future. Rather, by offering a graphic depiction of the blessing or torment likely to follow from present conduct, these messages sharply framed how individual and communal action was forming the future. Predictive prophecy is an invitation to affect divine action.
When the Son of Man Didn't Come, edited by Christopher Hays - Chapter 5, pg. 82-83
The problem that we have with Jesus' "failure" to return in the first century is that we have failed to understand the genre of the prophetic utterance. As explained in chapter 4, prophecy was not simple foretelling; although prognostication is part of the work of the prophet (as we saw in the "Mosaic" definition of prophecy), prophecy is about a good deal more than prognostication. The goal of prophecy is to address God's people about the state of their lives and worship, to encourage or to rebuke them by (inter alia) telling them what blessings await fidelity and what punishments await infidelity. But what actually does occur in the future is more often than not dependent upon the response of the people to the prophet; God is quite within his rights to renege on what the prophet foretold, depending on how the people responded. Since Jesus was a prophet (and we believe a great deal more than that as well!), we should not overlook the conditionality native to his prophetic utterances.
Our explanation, then, of Mark 9:1, Matt. 16:28, Luke 9:27 (and other texts like them) does not consist of redefining what it means to "taste death" or to see the "Kingdom come." We will not be reconstruing the significance of "generation" (Mark 13:30, Luke 21:32, Matt. 24:34) or what is entailed by the "coming of the Son of Man." Instead, we are reframing what it means for Jesus to "prophesy," on the basis of how prophecy works throughout much of Scripture and the ancient world.
Jesus' prophecy about the time of the end was not "wrong" because the veracity of his prophecy did not depend simply upon whether or not the end came. His prophecy about the timing of the end assumed that the people would respond rightly to his instructions about how to act in light of God's impending judgment. After all, Jesus' prophecies regarding the time of the end are all followed by imperatives to the disciples, demanding that they proclaim the good news to all the nations (Mark 13:10, Matt. 24:14); bear witness to Jesus fearlessly under trial (Mark 8:38, Matt. 10:32-33; Mark 13:11, Luke 12:14-15, Matt. 10:19-20); be ethically and existentially awake and alert (Mark 13:33-37, Matt. 24:42-45; Matt. 25:1-13). Insofar as people did not respond properly (as evidenced by the myriad of ethical rebukes contained in the New Testament epistles and the letters to the seven churches in Revelation 2-3), one might aver that it is not only understandable, but necessary that the end not occur within the prophesied time-frame.
When the Son of Man Didn't Come, edited by Christopher Hays - Chapter 11, pg. 259
The conditional and hortatory nature of prophecy explains a great deal of the non-fulfillment of the prophesied kingdom of God. The Messiah arrived preaching that the people of Israel should repent (Mark 1:15) in order that they might serve the kingdom of God that drew near. But the vast majority of his hearers, including the nation's leaders, rejected him so emphatically that they put him to death. One can fairly infer that this qualified as an inadequate response to the prophetic summons to repentance!
Yet, even the treason of God's people offered an occasion for divine grace. While the Lord could well have returned in those first months or years, seized his rebellious slave Israel, "cut him in pieces, and put him with the unfaithful" (Luke 12:46), he chose not to do so, "not wanting any to perish, but all to come to repentance" (2 Pet. 3:9; cf. Rom. 2:4). The final vindication of God's people was delayed, yes, but so was the final castigation, which would have fallen on a great many more souls.
This view seems to best accommodate what is actually seen in Scripture, as it would have been understood by those to whom Jesus was preaching. Of course, it can be formulated in different ways, and nuance can be added to it, but at the most basic level, the correct view of the passages in question seems to be to recognize that prophecy in Scripture is often conditional, and subject to change based on peoples' response.
The view that Jesus's second coming was delayed, though He and others predicted it would come in the first century, is one that grows out of the Biblical conception of prophecy, which accommodates, and even anticipates, God changing His mind in response to the actions of human beings.
The Old Testament provides the basis to make sense of the delay of Jesus's second coming. Without the context that it provides, constructing this case would be very difficult. However, when Biblical prophecy is examined as a whole, what is found is not a rigid, immovable concept of prophetic pronouncements, but one in which prophetic pronouncements are often by design an invitation to action and repentance, with God changing circumstances accordingly.