Three times in the Gospels (Matthew 24:34, Mark 13:30, Luke 21:32), when describing end-times events, Jesus says:
Matthew 24:34
34 Verily I say unto you, This generation shall not pass, till all these things be fulfilled.
Critics of the Bible assert that this is a failed prophecy, asserting that Jesus was telling the people that He was speaking to that their generation would not pass before all the events described in the chapter took place.
"This generation" is referring to the generation that witnesses the events being discussed, which becomes obvious when including the context:
Matthew 24:29, 33-34
29 Immediately after the tribulation of those days shall the sun be darkened, and the moon shall not give her light, and the stars shall fall from heaven, and the powers of the heavens shall be shaken:
33 So likewise ye, when ye shall see all these things, know that it is near, even at the doors.
34 Verily I say unto you, This generation shall not pass, till all these things be fulfilled.
Up to this point in the chapter, Jesus is describing the events accompanying His second coming, which includes many false prophets coming after Christ leaves (Matthew 24:5, 24:11, 24:24), world wars occurring (Matthew 24:6-7), the Gospel being preached to the entire world (Matthew 24:14), and a number of distinct prophetic events (Matthew 24:15, 24:29-31).
And it's only after the mention of "the tribulation of those days" (that He just got done describing) that He mentions "this generation".
A natural, uninterrupted reading of Matthew 24, Mark 13, or Luke 21 makes clear that the "generation" being referred to is the one that will witness the end-times events that are being discussed, not necessarily the current generation that was alive at that time, as each mention of "this generation" follows a description of events that are clearly future, but no precise time frame is given for them in reference to the present.
Jesus addresses the congregation - "when ye shall see all these things" - because these chapters are addressed directly to every believer from every generation up to and including the last generation:
Mark 13:35-37
35 Watch ye therefore: for ye know not when the master of the house cometh, at even, or at midnight, or at the cockcrowing, or in the morning:
36 Lest coming suddenly he find you sleeping.
37 And what I say unto you I say unto all, Watch.
Similarly, almost all of Jesus's sermons use this form of speaking directly to the audience ("ye"), yet we are to understand when reading the accounts, using common sense, that He is teaching precepts that apply to all of mankind.
Once the events being discussed happen, then Christ's second coming is very close. It will happen within the same generation that the events took place. Therefore, watch for those events.
This is not a failed prophecy, because "this generation" refers to the generation to which the things discussed in the immediate preceding context are happening to.