What is the evidence that the Angel of the Lord in the old Testament is probably Jesus? In Judges 6:11-12 we read:


  The angel of the Lord came and sat down under the oak in Ophrah that belonged to Joash the Abiezrite, where his son Gideon was threshing wheat in a winepress to keep it from the Midianites. 12 When the angel of the Lord appeared to Gideon, he said, “The Lord is with you, mighty warrior.”


In Judges 6:14 we read:


  14 The Lord turned to him and said, “Go in the strength you have and save Israel out of Midian’s hand. Am I not sending you?”


The Angel of the Lord appears to speak God's mind, and is interchangeable (by the writer) with the Lord himself. He doesn't speak as a messenger (as Gabriel does to Mary). 

One might conclude then that the person who knows the mind of God, and who the writer treats as interchangeable with God would be a pre-incarnation of Jesus. 

My question is: What is the evidence that the Angel of the Lord in the old Testament is probably Jesus? 

Clarification: This is asking generally across the whole old Testament - and is not limited to this passage.
Justin Martyr is probably the strongest early advocate for the view that the "Angel of the Lord" in the OT often refers to Christ.  In his Dialogue with Trypho, he argues that many supernatural appearances in the OT are manifestations of the second member of the Trinity.  One such example is that of the burning bush in Exodus 3:2-4, where reference to the "Angel of the Lord" and "the Lord" appear to switch (in a way similar to the Judges passage you quote).  He says:


  [I]n the vision of Moses, this same One alone who is called an Angel, and who is God, appeared to and communed with Moses. (chapter 60)


In this and other examples Justin equates the angel or mysterious man with God himself.

Justin finds more support from other church fathers when we turn to the mysterious men who are not specifically called "angels" in Scripture, but who appear to be supernatural.  Origen agrees that the mysterious figure in Joshua 5:13-15 is Christ, and bases this argument on the fact that Joshua worships him:


  Joshua recognized not only something from God but that which is God; for certainly he would not have worshiped unless he had recognized God.  For who else is chief of the army of the powers of God except our Lord Jesus Christ? ("Homilies on Joshua 6:2")1


Eusebius of Caesaria suggests that the close parallel in wording between this passage and Exodus 3:4-5 indicates "that this is no other than he who also spoke to Moses," that is, God.1

That said, this text does not refer to this man as an angel, so I don't know if you'd consider it a valid example.  Other fathers and commentators refer to this figure as an angel, do not ascribe deity to him, and explain Joshua's worship as mere "veneration" (John of Damascus).1

A similar episode occurs in Daniel 8:15-17.  I don't have a church father quote, but John Calvin says:


  We ought probably to interpret this passage of Christ, who is now called like a man, as formerly. (Daniel 7:13.) For he had not yet put on our flesh, so as to be properly entitled to the name of a man; but he was here like a man, because he wished to allow the holy fathers a taste from which they might understand his future coming as Mediator, when he should put on human nature as God manifest in flesh. (Commentary on Daniel, Volume II)


Note that Calvin is careful to say that this is not the second person of the Trinity incarnate, but that he is appearing "like a man."

1. Ancient Christian Commentary, page 31