They usually claim that the words "this generation" does not refer to the disciples of Jesus, but rather some future generation that witnesses the things he describes earlier in the chapter.
Yeah, forgot about that one. It doesn't hold any more water than the other excuses, because, among other reasons, other verses specify that Jesus spoke of contemporaries. Mark 9:1 says, "And he [Jesus] said unto them, Verily I say unto you, that there be some of them
that stand here, which shall not taste of death, till they have seen the kingdom of God come with power." Luke 9:27 is similar. It is the notion that people alive in Jesus's time would see such a thing, that led to the absurd tale of the Wandering Jew.
John 21:20-23 suggests that the Wandering Jew might be "the disciple that Jesus loved," traditionally the author of the Gospel himself. In this Gospel, it is suggested that this particular disciple would not die, a suggestion that Jesus neither confirms nor denies, saying, "If I will that he tarry till I come, what is that to you?"
Later mythologists came up with a more anti-Semitic version, and this is the one that "stuck."
The Wandering Jew supposedly got angry at Jesus for stopping in front of his property on Jesus's way to the cross. Jesus, beaten and bloody, supposedly said to this rude and unsympathetic Jew, "I will go, but YOU will tarry until I return." There are quite a few stories that include the Wandering Jew as character or a theme, including (perhaps) a Star Trek episode.
Anyway, the fact that the "future generation" rationale is at least as preposterous as the other supposed rationales seems to be no impediment against many who urge it.