When was Macbeth written?

Our best educated guess is that Macbeth was written between 1603-1606. Although some Shakespeare scholars believe that Macbeth was written as early as 1599, the circumstances surrounding the writing of the play and references in the play itself suggest that Macbeth was written after King James VI of Scotland succeeded to the English throne as King James I at the death of Queen Elizabeth I on March 24, 1603.
The question of who would succeed Elizabeth I was not resolved until very near her death, so Shakespeare had no way of knowing with any certainty who the next monarch would be. The many references in the play to King James and events that occurred after James became King suggest that Shakespeare wrote Macbeth no earlier than 1603.
It's clear that Shakespeare wrote Macbeth to please King James. James was keenly interested in witches, and he had written a book about witchcraft, Daemonologie, that was published in 1597 (and reprinted twice in 1603), so Shakespeare made witches important characters in the play.
King James believed that he was a descendent of Banquo. Shakespeare portrayed Banquo as a noble character, and made reference in the play to the King’s Scottish ancestry, particularly in the procession of kings scene in Act 4, Scene 1, lines 127-139. In the scene, apparitions of eight kings and Banquo appear to Macbeth. To Macbeth's dismay, all of the kings look like Banquo. The last king who appears to Macbeth holds a mirror that reflects a never-ending line of kings descending from Banquo, presumably including King James himself.
Shortly after his arrival in London in May, 1603, King James presented Shakespeare's acting company with a Royal Patent, giving the company the King's patronage and protection throughout England, and designated them "The King's Men." It's possible that the King commanded The King's Men to perform a play for him at court, and Shakespeare began writing Macbeth.
Unfortunately, the plague returned to London in June, 1603. Public gatherings were prohibited, the theatres were closed, The King's Men headed for the provinces to perform, and the King left London. The plague lessened for a brief time in the summer of 1604, which was long enough for the King to make a royal procession through London in which The King's Men participated, but the plague didn't fully subside in England until July, 1606, when The King's Men could prepare to perform Macbeth for the King.
Macbeth was first performed in the Great Hall at Hampton Court Palace in London on August 7, 1606, with James I and his brother-in-law, King Christian IV of Denmark, in attendance. This gives a timeframe for the writing of Macbeth between March 28, 1603, when James became King, and August 7, 1606, the date of its first performance..
There are clues in the play which might narrow the time during with Macbeth was written. For example, the Porter talks to an imaginary "equivocator" in his "Here's a knocking indeed!" speech in Act 2, Scene 3

Faith, here's an equivocator, that could
swear in both the scales against either scale;
who committed treason enough for God's sake,
yet could not equivocate to heaven: O, come
in, equivocator. (Act 2, Scene 3, lines 8-12)

This speech is believed to refer to Henry Garnet, a Jesuit priest who was one of the conspirators in the Gunpowder Plot to blow up Parliament and kill King James, his family, and as many member of Parliament as possible, which was to have occurred on November 5, 1605. The plot was discovered at the last minute, and the potential national disaster was avoided. At his trial in March, 1606, Henry Garnet was accused of "equivocation" (using vague and ambiguous language to conceal the truth and avoid self-incrimination), and equivocation in a law court under oath was considered treason.
If the Porter's speech actually refers to Henry Garnet, it's possible that Shakespeare wrote Macbeth only a few months before the first performance for the King in August, 1606.
There are other references in Macbeth to the Gunpowder Plot of 1605, the plagues of 1603-06 (Elizabethans believed that the plague was caused by "foul air"), and foul weather (there were storms and floods in the Spring of 1606) that help provide a context for Shakespeare's writing of Macbeth.
As with most things about Shakespeare's life and his plays, however, we can only make an educated guess about when Macbeth was written, but the most reasonable timeframe is 1603-1606.

William Shakespeare's Macbeth was probably written sometime between 1599 and 1606. The first performance of the play of which we have a record occurred in the summer of 1606, and was probably intended to flatter James I, who was himself Scottish. The main source for the play was Holinshed's Chronicles. The historical Macbeth MacFindlaech was King of Scotland from 1040 to 1059.