The word "generation" there in Greek is γενεα (genea), which can also refer to a family, stock, nation. (Strongs, definition 2b) The NASB also has a footnote here next to "generation" saying "Or race". I've always interpreted it, therefore, as meaning that the Jewish people will continue to exist until the second coming.
Another form of the same word, γενος, is used in 1 Peter 2:9 where the KJV says "But ye are a chosen generation..." and the NASB, NRSV, ESV, pretty much all the modern translations, say "But you are a chosen race..."
Some people object to this interpretation because of the other verses that are clearly talking about the people of that time not dying until they see the kingdom come.
Matthew 16:28 "Verily I say unto you, There be some standing here, which shall not taste of death, till they see the Son of man coming in his kingdom."
Mark 9:1 "And he 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 "But I tell you of a truth, there be some standing here, which shall not taste of death, till they see the kingdom of God."
But I maintain that these are about the coming of the kingdom in the form of the establishment of the church on Pentecost, whereas Matthew 24:34 is about the end of the world. And so I believe they are speaking about different groups of people. You will notice also that these other verses don't use the word "generation."