There are more instances of dramatic irony in Macbeth than those listed in the two previous answers. Below is a list of examples that have not yet been mentioned.
Act 1, scene 3: "a greater honour"
After Macbeth and Banquo have met the weyard sisters, Angus and Ross brings news from king Duncan. Ross says,
And, for an earnest of a greater honour,
He bade me, from him, call thee thane of Cawdor
Ross's words "greater honour" probably refer to Duncan's "hyperbolic promises" (G. K. Hunter, page 143). Unlike the audience, Ross does not know that Macbeth has heard he will become king and that his words will make Macbeth think of the third prophecy.
Act 1, scene 4: "O worthiest cousin!"
There's no art
To find the mind's construction in the face:
He was a gentleman on whom I built
An absolute trust.
Enter MACBETH, BANQUO, ROSS, and ANGUS
O worthiest cousin!
The first four lines of this speech by Duncan are about the previous thane of Cawdor, who had rebelled against him. The last line is spoken to Macbeth, the new thane of Cawdor, who has been promised kingship. Within a single speech, Duncan moves from condemning the previous thane of Cawdor to trusting the new one. This is dramatic irony unless the audience thinks that Macbeth will simply wait for Duncan's natural death (and possibly the death of Duncan's sons).
Act 1, scene 4: the establishment of primogeniture
Later in the same scene, Duncan says,
We will establish our estate upon
Our eldest, Malcolm, whom we name hereafter
The Prince of Cumberland
These words are usually interpreted as establishing primogeniture in Scotland. Under the system of tanistry, which also existed in Scotland, Macbeth may have been a potential successor. The transistion from tanistry to primogeniture in Scotland started under the House of Dunkeld, of which Duncan I was the first king. More importantly, even for spectators unaware of tanistry, Duncan unwittingly puts an obstacle on Macbeth's path to the Scottish throne.
Act 2, scene 4: Malcolm and Donalbain's flight
By the same logic that made Macbeth kill Duncan, he would also need to kill Malcolm, the designated heir, in order to become king. By fleeing from Scotland, Malcolm and Donalbain unwittingly help Macbeth achieve his goal.
Act 3, scene 4: "Were the graced person of our Banquo present"
During the banquet scene, Macbeth says about Banquo:
Here had we now our country's honour roof'd,
Were the graced person of our Banquo present;
Who may I rather challenge for unkindness
Than pity for mischance!
Macbeth is unaware that Banquo has walked in behind his back and is sitting in his place.
Another instance of dramatic irony follows immediately: Ross talks about Banquo's absence without knowing Macbeth has had him killed. Much of the rest of the scene relies on this, since only Macbeth and the audience are aware of Banquo's ghost.
Act 3, scene 6: "Banquo ... / Whom ... Fleance kill'd"
The same fallacious logic that led Macduff to conclude that Malcolm and Donalbain were behind Duncan's death (see Gareth Rees's answer) is applied to Fleance: he has fled so he is suspected of killing his own father. The audience knows that he fled to save his own life, just like Duncan's sons had done.
The play's first scenes contain a number of verbal echoes—characters who repeat words they don't know have been spoken by others before—which may also be interpreted as dramatic irony in a looser sense.
- Macbeth's words "So foul and fair a day I have not seen" (Act 1, scene 3) echo the weyard sisters' words "Fair is foul, and foul is fair" (end of Act 1, scene 1).
- Ross's words "hail, most worthy thane!" (Act 1, scene 3) to some extent echo the weyard sisters' "All hail, Macbeth! hail to thee, thane of Glamis" and other uses of the word "hail" by them in the same scene.
- Shakespeare: Macbeth. Edited by G. K. Hunter. The New Penguin Shakespeare. Penguin, 1967.