1 Corinthians 6:18, Hebrews 12:16, and Revelation 14:8 simply mention sexual immorality without really giving a bigger sense what what they mean. A first thought might be that they are cleverly leaving out the details. However, I think if we look at other verses, we can get a pretty good idea what the bible has in mind when it says "sexual immorality".
Another example of sexual immorality is adultery, having sex with someone else's spouse (although I'm sure the bible would say "with someone else's wife"). Hebrews 13:4, James 4:4, and Revelation 2:14,20-22 all warn directly of adultery. It's hard to argue with that, don't screw around with married people. Moving on.
A big theme is purity, the bible has a fair bit to say about abstinence before marriage. Ephesians 5:3-5, Philippians 4:8, Colossians 3:5, and Revelation 14:4 all reference purity or virginity. There is an angle from which this could have a reasonable basis, and that is from the perspective of a parent. When you have sex you up the ante emotionally quite a bit, and if things fall apart it's that much worse. It makes sense for a parent to want to prevent such a thing in their children. Furthermore, before the age of birth control, you are talking about the likelihoods of your kids having kids before they are ready. You certainly don't want that. However, by eliminating sex before marriage, you are probably going to encourage people to get married before they are really ready for such a commitment. Well, this could easily be a whole blog post on its own, I'm going to move on.
The biggest problem I have with the bible in regards to it's position on sexuality, is all of the verses against passion and lust. These feelings are quite natural, and telling people they are bad for having them can really screw them up. I think telling a teenage boy that he is evil for getting a boner is fucking abuse. It's absolutely ridiculous. Verses against passion or lust: Colossians 3:5, 1 Thessalonians 4:4-5, 2 Timothy 2:22, 1 Peter 4:3, 2 Peter 2:9-10, and 1 John 2:16. What could the consequences of passion or lust be? 2 Peter 2:2 suggests that following your sensuality will lead you to blaspheme, and we know from before that blasphemy is the one unforgivable sin. It might not be clear exactly how sensuality and blasphemy are connected, but 2 Peter 2:18 expands on the idea and explains that the unrighteous will use their sensuality to entice people away from God.
One final verse I will leave you with, Matthew 5:28 which says that if you simply have lust, you have already committed adultery in your heart. Good ol' thought crimes. These ideas were definitely among the most damaging to me when I was growing up, to think that an errant thought is just as bad as the actual act, how can you control something like that? Telling a teenage boy that he is bad for getting aroused when he sees an attractive woman walk down the street in a low cut dress? Now that is fucking evil!