I find this wording interesting in Genesis 5:24 (NIV) (my emphasis)
Enoch walked faithfully with God; then he was no more, because God took him away.
To me, this means God took Enoch to heaven. So, because sinful mortals can't be around God does this imply that Enoch was sinless?
No. Enoch sinned just like the rest of us.
He was taken to heaven because Christ's righteousness was imputed to him, just like it is imputed to us.
Christ's death and resurrection saved all believers past and present, there is no need for any other explanation of righteousness.
The best answer that I've ever heard was from Paul Washer who said this:
Enoch walked with God for so long that when it was time to go home, God said: "You know what Enoch, you've been walking with me for so long, look we're closer to my home then yours. Why don't you just come home with me."
We know that All men have sinned and all men fall short of the glory of God.
But faith (trust) in Christ and love for others is what pleases the lord.
I will let the Scriptures speak for themselves:
As it is written, There is none righteous, no, not one: There is none that understandeth, there is none that seeketh after God. They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one... For all have sinned, and come short of the glory of God.. Romans 3:10, 11, 12, 23
Going by these passages which are an allusion from the Old Testament it is explicit that Enoch had committed some sin and was saved by the Righteousness of Christ.
The Bible says that:
By faith Enoch was translated that he should not see death; and was not found, because God had translated him: for before his translation he had this testimony, that he pleased God. But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him. Hebrews 11:5,6
Genesis 5:24 tell us a brief narration of a patriarch. Details are not available because the historical rigor was not important in the OT. Life and acts of Enoch were not mentioned by the author of the Epistle to the Hebrews (11:5), who notes only the faith of the Patriarch the price to pay to "not see death". We can take the example of Eliah in 2 Kings chapter two: he was a man with fears and human deffects, but "God took him" (i.e. Genesis 5:22-29).
C Rags answer is the best one so far because it is based on Scripture (Unfortunately as of now I can't comment neither vote up on his answer).
If I am to give another answer, I would also use the Scripture beginning in Romans 5:12-14 (KJV):
12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: 13 (For until the law sin was in the world: but sin is not imputed when there is no law. 14 Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come.
This text (and its continuation) establishes Adam as the head of the natural race, and "him who was to come" (=Jesus) as the head of the spiritual race. It also establishes that each one has an effect over all the ones born in their respective race. In the case of Adam, sin is one such thing; death is the other one.
There are several genealogies in the Bible that establish Enoch as being a descendant of Adam. As such, he inherited sin and death from Adam.
Verse 14 of the quoted text says death reigned from Adam to Moses, as to establish this concept of race headship, meaning people were dying not because they disobeyed God in the same fashion as Adam did: "that had not sinned after the similitude of Adam's transgression", or that there was a law for them to trespass and be condemned of death, but they were dying simply because they were born into the race of Adam.
The very text of Genesis 5 begins saying that Adam was first created in the image/likeness of God. Then we know he fell and became a sinner because he ate the fruit of the wrong tree, then Genesis 5.3 says he "begat a son in his own likeness, after his image" (no longer in God's image, but in his sinful image):
1 This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him; 2 Male and female created he them; and blessed them, and called their name Adam, in the day when they were created. 3 And Adam lived an hundred and thirty years, and begat a son in his own likeness, after his image; and called his name Seth.
Enoch, being listed as a descendant of Adam, was no different that Cain and the others who died, in the sense of having inherited the sin problem and the death problem from Adam. Is was only Jesus, who was born from a virgin Miriam, that did not appear as a human descendant of Adam (recall from verse 3 only the male passes on the sin and death nature). Instead, he's the first one of the spiritual race, and heads up the spiritual race. The others follow suit by means of a spiritual union with Christ in crucifixion, burial and resurrection, that occurs when they born again.
Now one can cite Romans 5:14 and argue that Enoch was the only one between Adam and Moses that did not die. Genesis 5 explains why he didn't die: it was not because he wasn't born with a sin and death problem, the text plainly states he was a descendant of Adam, but because (as wax eagle properly put) God imputed Christ's righteousness on him and then took him up.
