Biblical Rape?

There are many mentions of types of rape in the Bible, but part of the problem in distinguishing them is that the Bible generally uses the normal word for "have sex with" to describe "rape." Typically, it is the circumstances surrounding the sex that distinguish it as rape. In short, rape is never okay. I'll address each of the passages you mentioned individually, as well as one you didn't that pertains to the subject.

Genesis 19:6-8
This is clearly an instance in which Lot offered his daughters to be raped by the mob, but this does not justify the rape. Rather, it is an example of the weakness and sin for Lot. Although the New Testament describes him as "righteous Lot" (2 Pet. 2:7), it does not do so on the basis of this action but on the basis of his torment at living in their society. In other words, his conscience more than his actions bore witness to his righteousness. His offering of his daughters itself was an act of desperation, and a wrong act at that - and I would challenge any father to deny that fact. Can you imagine offering your own daughter to be raped? Doesn't every fiber of your being rise up and fight that idea? Well, that was supposed to be how the original audience reacted to this information too. They weren't supposed to think, "Oh, then I guess it's okay." They were supposed to react the way every father in the world should react, whether regenerate or not. They were supposed to be horrified and to think, "What!? You mean even the 'righteous' people in the city behaved that way? No wonder God wiped them out!"

Notice also that Lot was not so righteous that God would have spared the city for his sake. In Genesis 18:17ff. God tells Abraham that he will spare the city for the sake of the righteous in it, but the angels warn Lot that if he does not flee he will be destroyed along with the city (Gen. 19:15-16). This is an indication that Lot himself was not all that righteous; he did not "earn" his salvation from destruction, but God was compassionate to him anyway. That he and his family were less than noble is also indicated by the fact that his wife disobeys the angels and is turned into a pillar of salt (Gen. 19:26), and by the fact that his daughters get him drunk and sleep with him (Gen. 19:30-38). Lot was "righteous", but not because he was pure.

Further, the Bible itself offers a bit of commentary on this episode in the literary parallel between Genesis 19 and Judges 19 (the rape of the Levites concubine). In that story, the events are quite similar and the literary parallels are many and explicit. The clear intent of the author was to recall the story of Genesis 19. But the events of Judges 19 are all the more terrible because they take place in Israel (v. 30) rather than in Gentile territory. There the rape is clearly perceived as grossly wicked - so wicked that the refusal of the town to submit to discipline provokes a war (chs. 20-21). The point for our discussion is simply that the obvious literary parallel portraying the rape of the Levite's concubine as sinful depends upon Lot's act in Genesis 19 being sinful.

Numbers 31:17-18
These virgins were not to be raped; they were to be married. Deuteronomy 21:10-14 gives a fuller description of this law.

Deuteronomy 22:28-29
First, it is important to recognize that these very verses prescribe a punishment of sorts for the crime of rape, namely the payment of a fine and indissoluble marriage to the raped woman (marriages were normally dissoluble under the proper circumstances). Second, the verses immediately preceding these indicate the death penalty for rapists and adulterers. Vv. 23-24 describe consensual sex with an engaged woman, in which case there is no rape and both parties are put to death. Vv. 25-27 describe the rape of an engaged woman, in which case the lack of the woman's consent is indicated by the fact that the man "forces" her, and the assumption that she cried out for help. Here the rapist is put to death.

It is in this context of having already established that rape is a capital offense that vv. 28-29 then speak of a man who has probably non-consensual sex with an unengaged virgin. The crime here is a slightly lesser crime because there is no offended husband. Moreover, the lesser penalty also reflects an attempt to mitigate the damages of the crime. That is, in this case the offender and the woman are both eligible for marriage, and it is unlikely that anyone will want to marry the woman because she is no longer a virgin. She will thus have no one to provide for her later in life, and will have not chance of posterity. This would increase her victimization. Practically speaking, the offending man is more use to her alive than dead. He is allowed to live in order that he might make lifelong restitution to the woman.

Isaiah 13:16
This text indicates that the armies of the Lord rape the wives of those God judges. But even this does not validate rape. Rather, the point is that those who act wickedly toward the Lord's people will themselves be treated wickedly by foreign invaders. Just as in the case of the men God ordained to kill Jesus, however, the rapists in this case will not go unpunished. God will judge them as well, despite the fact that he uses their wickedness for his own ends.