The gospels of Matthew, Mark, and Luke all record this particular passage, though there are a few slight differences. Matthew says there are some who won't taste death until the "Son of Man" comes into his kingdom. Mark adds the comment that the kingdom will come with "power." While Luke keeps it pretty plain and simple. However, these differences seem only to be stylistic variances of the three authors.
To understand Jesus' words it is important to look at a couple of contexts. First, what did the writers understand Jesus to mean; second, what did Jesus himself mean; and third, what does this mean in the larger context now that nearly two millennia has passed since the words were spoken.
As we look at the whole of the New Testament, especially the Gospels and the letters of Paul (the majority portion of the New Testament), it is clear what the respective writers believed Jesus meant. Jewish apocalyptic literature had long referred to "the day of the Lord." On this day, or so the literature says, God will send wrath against all those who opposed and oppressed the nation of Israel and that Israel would become the world's leading nation. During this time the designees of God would rule with true justice and mercy according to the prescripts of the law. Other Jewish writers added that the day of the Lord included a general judgement, the end of the world as we know it, and the beginning of a new world-a kingdom of God. The writers of the New Testament clearly linked this apocalyptic "day of the Lord" with Jesus' words and assumed Jesus would be the chosen one who would rule in the new kingdom that was to come. And thus, when Jesus spoke these words, they believed he spoke of this kingdom coming before their deaths.
Jesus, on the other hand, may have had a different understanding of the kingdom of God. In Luke he says, "Being asked by the Pharisees when the kingdom of God was coming, he answered them, 'The kingdom of God is not coming with signs to be observed; nor will they say, "Lo, here it is!" or "There!" for behold, the kingdom of God is within you'" (Luke 17.20-21). Indeed, the most common references Jesus makes about the kingdom of God is that it was a present reality, not a future coming. In the fuller context of the gospels it seems that Jesus' understanding of the kingdom of God was that the kingdom was based on the relationships of those who followed the "king," i.e., Jesus. Therefore, when Jesus spoke of those who would not die before they saw the kingdom of God coming, Jesus apparently meant that they would become participants in a metaphysical kingdom that was based on his life and his teachings.
Indeed, as the writers of the New Testament grew older, it seems they may have softened their view of the coming day of the Lord and chose to embrace Jesus' view of the kingdom.
As we look back upon the words of Jesus today, scholars are somewhat torn as to his exact meaning. Some scholars suggest that Jesus himself thought that he'd be ushering in the day of the Lord in short order following the cross-resurrection event, but that he was mistaken.
Others, including the Jesus Seminar scholars, believe that Jesus never actually suggested that he was to have any part in the day of the Lord. Instead, the early church applied the Old Testament apocalyptic literature to the life of Jesus and thus projected Jesus into the scenario.
Still others think the coming of the kingdom refers to the Pentecost event (recorded in Acts 2) where the Spirit of God was visited upon the early church leaders and they began proclaiming the life and teachings of Jesus freely among society.
And finally, some believe Jesus meant what he said and that the kingdom of God was, and is, a present reality; that people can participate in that kingdom today through belief, faith, and practice; and that the kingdom has indeed come in power-giving followers of Jesus in the kingdom of God the power of life.