First, a timeline.
The prohibition on incest was not given until well after creation. At least as far as traditions that believe Genesis to be a historical account are concerned, Adam and Eve were the first two humans on earth, they procreated, had a whole bunch of sons and daughters, some of which paired. For more on this see:
Did Adam and Eve's Progeny Commit Incest?
There was actually another bottleneck in the human family tree much later at the time of Noah. While Noah's direct offspring brought their spouses along for the ride, his grandchildren would have been limited to marrying each other, so cousins if not siblings.
The commands about not marrying family relations that were too close didn't come for another couple thousand years, about the time of the Mosaic law that was to govern Israel after they were taken out of Egypt.
The prohibition is later affirmed and renewed in various places and still in effect today and won't be changed again.
So who's included?
There is a run down of relationships that are considered too close or otherwise off limits here:
Leviticus 18:6-18 (ESV)
6 “None of you shall approach any one of his close relatives to uncover nakedness. I am the Lord. 7 You shall not uncover the nakedness of your father, which is the nakedness of your mother; she is your mother, you shall not uncover her nakedness. 8 You shall not uncover the nakedness of your father's wife; it is your father's nakedness. 9 You shall not uncover the nakedness of your sister, your father's daughter or your mother's daughter, whether brought up in the family or in another home. 10 You shall not uncover the nakedness of your son's daughter or of your daughter's daughter, for their nakedness is your own nakedness. 11 You shall not uncover the nakedness of your father's wife's daughter, brought up in your father's family, since she is your sister. 12 You shall not uncover the nakedness of your father's sister; she is your father's relative. 13 You shall not uncover the nakedness of your mother's sister, for she is your mother's relative. 14 You shall not uncover the nakedness of your father's brother, that is, you shall not approach his wife; she is your aunt. 15 You shall not uncover the nakedness of your daughter-in-law; she is your son's wife, you shall not uncover her nakedness. 16 You shall not uncover the nakedness of your brother's wife; it is your brother's nakedness. 17 You shall not uncover the nakedness of a woman and of her daughter, and you shall not take her son's daughter or her daughter's daughter to uncover her nakedness; they are relatives; it is depravity. 18 And you shall not take a woman as a rival wife to her sister, uncovering her nakedness while her sister is still alive.
There are also related reiterations of this in Leviticus 20:11-21, Deuteronomy 22:30, and Deuteronomy 27:20-23.
Basically we have:
- No parents (including inlaws or anyone intimate with parents)
- No children (or anyone intimiate with them, son inlaw, dauther inlaw, etc)
- No siblings (including half siblings)
- No grandchildren (or any other level of offspring)
- No aunts, uncles (or their intimates)
- No inlaws (brother inlaw, sister inlaw)
Also included here is having relationships with someone who is any of these connections to somebody you've been intimate with - with a notable exception for siblings if the original parter is diceased. In other words if your wife dies, marrying her mother (or daughter even if the child isn't yours) is not an option, but if she had a sister you could marry her. Another case worth mentioning is Levirite marriage where marrying your siblings spouse is allowed in the vent your sibling has died.
Notably absent from the list of specifically prohibited relationships is first-cousins. Some people make the case that these would be covered in the more umbrella statement of Lev 18:1 where "any close" (litterally blood) relatives are off limits. Another factor to consider here is that it is illegial in some states and countries, a factor Christians usually consider binding (although they may not consider all things allowed by the state as permissable, they usually consider those prohibited by the state as off limits). The same social taboos about first-cousins that exist in the West are not nearly as strong in the Middle East. How Christians view that case in practice, at least to some extent, mirrors the cultural understanding.
That this assortment of off-limit relationships was still expected of Christians in the New Testament can be seen here:
1 Corinthians 5:1 (ESV)
5 It is actually reported that there is sexual immorality among you, and of a kind that is not tolerated even among pagans, for a man has his father's wife.
Are these views consistent across sects?
Almost, but not quite.
As I mentioned above, there is some variation in understanding when it comes to doubtful cases not specifically listed above such as first-cousins or step siblings:
Does the Old Testament law prohibit marriage among step siblings?
However the differences in understanding tend to be isolated more to regions than to sects.
There are of course a number of small sects with very different views on family relationships in general. (See LDS, it's sects and polygamy). However as a broad generalization incest is widely defined in roughly the same way as above, partly because the Scriptural prohibition is so specific.
Christians generally consider incest to cover a wide variety of family relationships.