1) Famine appears 84 times in the Old Testament, most frequently found in Genesis, then Jeremiah
2) Famine appears 10 times in the New Testament, referring to past famines in the Old Testament or famines that will occur in the end times, one prediction of a famine during the reign of the Roman Emperor Claudius, and the following verse -
3) Believers in Christ have this promise in Romans 8:35 concerning famine: "Who shall separate us from the love of Christ? Shall trouble or hardship or persecution or famine or nakedness or danger or sword?... No, in all these things we are more than conquerors"
4) Famine is one of four ways that the Lord punishes the breakers of His covenant in the Old Testament (see Leviticus 26:12-25). The other punishments are disease/plagues, defeat by enemies, and wild animals (such as locusts). These are all repeated in Revelation as means of punishment, along with a fifth - natural disasters. The Lord causes these disasters so that people will repent and seek Him.
5) The verses in Amos are the only time this particular type of famine is ever mentioned; also it is the last mention of famine in the Old Testament.
Here's my conclusion based on my study. We know that there was a gap of about 400 years between the last prophet of the Old Testament and the first of the New Testament, John the Baptist. This gap very likely describes the famine of the hearing of the Word of the Lord predicted by Amos. For 400 years, the Israelites went without hearing anything from the Lord. Of course they still had the written prophecies; but the prophecies about the Messiah were still unfulfilled. This famine, God's silence, was a punishment for their continued disobedience as evidenced over and over again in the books of the major prophets and the minor prophets.
After such a long famine, when a prophet finally did appear proclaiming the word of the Lord, the coming of the Messiah, they should have been very eager to hear!
Some of the Jews were ready to hear and repent, but most of them weren't. Most of them rejected Jesus when he didn't fit their idea of what a Messiah should be. It wasn't until after his death, until the Lord sent the Holy Spirit, that they began to understand (in large numbers) that Jesus really was the Messiah and that his death provided for our salvation.
Jesus is the bread of life. Matt 4:4 "Man does not live on bread alone, but on every word that comes from the mouth of God."
Jesus is the Word. John 1:14 "The Word became flesh and dwelt among us."
It is certainly possible to experience a famine of hearing the Word, even today - by purposefully rejecting the message of the Gospel, rejecting Christ, by worshiping the creation instead of the Creator (Romans 1:25). Though a warning of famine such as the one in Amos is not repeated in the New Testament, there are some similar warnings: Luke 17:22 "The time is coming when you will long to see one of the days of the Son of Man, but you will not see it." And again: John 7:34 "You will look for me, but you will not find me; and where I am, you cannot come."
Personally I've experienced a few famines of my own - when I get too busy for church, or to open my Bible on a regular basis. Eventually I get to the point where I am lonely, discouraged, feeling overwhelmed - and then I remember that I've been starving myself of the Bread of Life. I am so thankful that when I remember to seek the Word again, God does not make me stagger from sea to sea searching, and yet never finding. For believers, we have that marvelous promise in Romans 8:35-37. I am so thankful.