Is illness sometimes a result of a sin?

Yes: This is very closely related to cause and effect, some cause is of sin - some cause (of illness) is not of sin. i.e - (removed example of sin -> illness, need a better one)However, eating only processed food or uncooked food because of lack of knowledge on how to cook, nutrition etc, (not sin) can still lead to getting sick, cancer, etc...illness (and for the later one, there are many things we don't know, that we don't understand, that may effect our body).

However, it is very intriguing to point out a fact that there are people who intentionally sin as part of their life style with exceptional health, wealth and well-being.

So this question really fall under the umbrella of of the fall like mentioned above, that all good or bad are susceptible to the effects of "darkness" (evil, devil):

(or the opposite, that God will let "light" be shown to the good and the bad)

http://www.thefaithlog.com/2005/08/rain-for-just-and-unjust.html

Matthew 5:45

Easy-to-Read Version (ERV)

45 If you do this, you will be children who are truly like your Father in heaven. He lets the sun rise for all people, whether they are good or bad. He sends rain to those who do right and to those who do wrong.

Yes it is. But you will not go to hell cause you got sick. If any one tells you that look at them and say every BOLDLY get behind me satan. This is the hard part about the word of God. I said word of God, He watches over his word to perform it, not his will but his word, he uses his word to do his will. Read it again. When you understand that it is the word that is being done that is when you will make your words line up with his "God's" will and the sickness and the sin will leave. Greater is he that is in you than he that is in the world. This has to be growing in you before it will produce the harvest. That is what you looking for. It is right there Matthew 13, Mark 4 and Luke 8 sow the word of God reap the will of God and that is what over comes the world.

Death itself is a consequence of original sin as are all sicknesses. Specifically, it does seem that some sicknesses are a direct result of sin, sometimes as a byproduct but other times as a direct judgment of God.

Paul wrote to the Romans points out that some of the believers were taking communion in an unworthy manner. He then notes that this results in judgment, and then states that this is why some people were sick and some had even died.

27 Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty concerning the body and blood of the Lord. 28 Let a person examine himself, then, and so eat of the bread and drink of the cup. 29 For anyone who eats and drinks without discerning the body eats and drinks judgment on himself. 30 That is why many of you are weak and ill, and some have died. 1 Corinthians 11:27-31 ESV

So, yes, some sickness can certainly be a direct judgment of God. Of course, some sins expose people to sicknesses to which they would otherwise not be exposed. In such cases, it would probably be better considered just a consequence of sin rather than a specific judgment of God.

Alternatively, we know that some sickness is not the result of any sin at all, as Jesus told the disciples about the man who was born blind:

As he passed by, he saw a man blind from birth. 2 And his disciples asked him, “Rabbi, who sinned, this man or his parents, that he was born blind?” 3 Jesus answered, “It was not that this man sinned, or his parents, but that the works of God might be displayed in him. John 9:1-3 ESV

If it is, in fact, a judgment of God, it is good to note the reason for the judgment. God disciplines us for our good, as a father disciplines his own children.

And have you forgotten the exhortation that addresses you as sons? “My son, do not regard lightly the discipline of the Lord, nor be weary when reproved by him. 6 For the Lord disciplines the one he loves, and chastises every son whom he receives.” Hebrews 12:5-6 ESV

Ailments like sickness and bodily weakness are a consequence of the Fall, natural companions to the physical state in which we live. Not all are a punishment or result of sin, but some certainly may be.

James Talmage, a Biblical scholar in the early 1900s, has this to say on the matter (in Jesus the Christ), considering the healing of a man sick of the palsy:

The incident demands our further study. According to one of the accounts, the Lord's first words to the afflicted one were, "Son, be of good cheer," followed directly by the comforting and authoritative assurance, "Thy sins be forgiven thee." The man was probably in a state of fear; he may have known that his ailment was the result of wicked indulgences; nevertheless, though he may have considered the possibility of hearing only condemnation for his transgression, he had faith to be brought. In this man's condition there was plainly a close connection between his past sins and his present affliction, and in this particular his case is not unique, for we read that Christ admonished another whom He healed to sin no more lest a worse thing befall him.

We are not warranted, however, in assuming that all bodily ills are the result of culpable sin, and against such a conception stands the Lord's combined instruction and rebuke to those who, in the case of a man born blind, asked who had sinned: the man or his parents, to bring so grievous an affliction upon him, to which inquiry our Lord replied that the man's blindness was due neither to his own sin nor to that of his parents.

In many instances however, disease is the direct result of individual sin. Whatever may have been the measure of past offense on the part of the man suffering from palsy, Christ recognized his repentance together with the faith that accompanied it, and it was the Lord's rightful prerogative to decide upon the man's fitness to receive remission of his sins and relief from his bodily affliction. The interrogative response of Jesus to the unuttered criticism of the scribes, Pharisees, and doctors has been interpreted in many ways. He inquired which was easier to say, "Thy sins be forgiven thee," or to say, "Arise, and take up thy bed, and walk."

Is it not a rational explanation that, when spoken authoritatively by Him, the two expressions were of allied meaning? The circumstance should have been a sufficient demonstration to all who heard, that He, the Son of Man, claimed and possessed the right and the power to remit both physical and spiritual penalties, to heal the body of visible disease, and to purge the spirit of the no less real malady of sin. In the presence of people of all classes Jesus thus openly asserted His divinity, and affirmed the same by a miraculous manifestation of power.

(I had to manually add punctuation, and this may not be a perfect transcription; I also inserted some paragraph breaks!)