What passages of Scripture were used by the popes and crusaders to justify the Crusades? What passages of Scripture were used by the popes and crusaders to justify the Crusades? 

I am specifically interested what the individuals that were contemporary to the crusades were saying. For the purpose of this question, I am only interested in arguments based in Scripture.
St. Bernard of Clairvaux is perhaps the most well known promoter of the Crusades. He is credited for sparking the 2nd Crusade by writing very convincing letters to the Kings of Christendom. On Christmas Day, 1144, the Seljuk Turks captured Edessa, chief city of one of the Christian principalities set up by the First Crusade. Appeals for help went at once to Europe, for the position of all Christians in Syria was jeopardized. King Louis VII of France announced his intention of leading a new crusade, and the Pope commissioned Bernard to preach the Holy War. 

Bernard sent a number of theologically charged letters to the various Kings and Queens of Christendom asking for support on behalf of the Church.  His main selling point was the biblically sound cause of liberating the Jews from Muslim oppression, and also for their protection from rogue Crusaders.  

In a letter written in 1146AD to Eastern France and Bavaria, Bernard promotes the 2nd Crusade by appealing to the role of Jews in God's plan of salvation:


  Besides, brethren, I warn you, and not only I, but God's apostle,
  "Believe not every spirit." We have heard and rejoice that the
  zeal of God abounds in you, but it behooves no mind to be wanting in
  wisdom. The Jews must not be persecuted, slaughtered, nor even driven
  out. Inquire of the pages of Holy Writ. I know what is written in the
  Psalms as prophecy about the Jews. "God hath commanded me," says the
  Church, "Slay them not, lest my people forget."
  
  They are living signs to use, representing the Lord's passion. For
  this reason they are dispersed into all regions, that now they may pay
  the just penalty of so great a crime, and that they may be witnesses
  of our redemption. Wherefore the Church, speaking in the same Psalm,
  says, "Scatter them by thy power; and bring them down, O Lord, our
  shield." So has it been. They have been dispersed, cast down. They
  undergo a hard captivity under Christian princes. Yet they shall be
  converted at even time, and remembrance of them shall be made in due
  season. Finally, when the multitude of the Gentiles shall have entered
  in, then, "all Israel shall be saved," saith the apostle.
  Meanwhile he who dies remains in death.


Elsewhere, he writes to the Archbishop of Mainz:


  The fellow you mention in your letter [a monk named Raoul, who had
  urged violence against Jews as the Second Crusade was being organized]
  has received no authority from men or through men, nor has he been
  sent by God.
  
  Does he consider himself greater than our father Abraham who laid down
  his sword at the bidding of him by whose command he took it up? Does
  he consider himself greater than the Prince of the Apostles who asked
  the Lord: "Shall we strike with our swords?" He is a fellow full
  of the wisdom of Egypt which is, as we know, foolishness in the sight
  of God. He is a fellow who answers Peter's question differently to the
  Lord who said: "Put back thy sword into its place; all those who
  take up the sword will perish by the sword." Is it not a far better
  triumph for the Church to convince and convert the Jews than to put
  them all to the sword? Has that prayer which the Church offers for the
  Jews, from the rising up of the sun to the going down thereof; that
  the veil may be taken from their hearts so that they may be led from
  the darkness of error into the light of truth, been instituted in
  vain? If she did not hope that they would believe and be converted, it
  would seem useless and vain for her to pray for them. But with the eye
  of mercy she considers how the Lord regards with favor him who renders
  good for evil and love for hatred. Otherwise where does that saying
  come in, "Not for their destruction I pray," and "When the
  fullness of the Gentiles shall have come in, then all Israel will be
  saved," and "The Lord is rebuilding Jerusalem, calling the
  banished sons of Israel home"? Who is this man that he should make
  out the Prophet to be a liar and render void the treasures of Christ's
  love and pity? This doctrine is not his own but his father's. But I
  believe it is good enough for him, since he is like his father who
  was, we know, "from the first a murderer, a liar, and the father of
  lies."


Of course we know from history that the 2nd Crusade was an overall failure. It is debatable whether or not the Pope's commission for St. Bernard to preach this failure was a good idea. Whatever the case may be, St. Bernard carried out his mission as a loyal servant to both the Church and to Sacred Scripture, ultimately becoming a canonized Doctor of the Church.

The Crusades began with Pope Urban II's speech at the Church Council at Clermont in 1095. The Crusades, as institutionalized Holy War with papal sanction against the perceived enemies of Christendom, ended in 1798 with the expulsion of the Hospital of St John from Malta by Napoleon.

St. Bernard's story is just one little chapter in a long book...