Does Macbeth have a conscience?

Macbeth is confronted by his conscience at several points in the play, particularly when faced with the original prophecy given to him by the "three weird sisters". Upon hearing the information that these haggard and strange characters give to him, he asks himself, in one of several soul-searching asides:
"The Prince of Cumberland! That is a step
On which I must fall down, or else o'erleap,
For in my way it lies. Stars, hide your fires;
Let not light see my black and deep desires!"
It is here that we see the presence of a conscience in Macbeth, because even though he is already plotting the murder of Duncan, he is aware of his "black and deep desires" and is, on some level, ashamed of them. It is this shame that signifies an awareness of the difference between good and evil: a conscience.

Macbeth undoubtedly has a conscience. Throughout Shakespeare's play, Macbeth's conscience is in continual conflict with his political ambitions.
Conscience is often confused with guilt. Macbeth has both, but it helps to distinguish between the two when analyzing Macbeth's character and behavior. Conscience is our innate sense of right and wrong. Our conscience guides our decision-making process, particularly when the decision involves considerations of right and wrong. Guilt arises from a realization that we've done something wrong or that we've harmed someone, whether we intended to harm them or not. Conscience comes into play before we do something. Guilt is the feeling we have after we've done something that our conscience tells us was wrong.
Lady Macbeth gives us insight into Macbeth's character the first time we see her:

[Y]et do I fear thy nature;
It is too full o' the milk of human kindness
To catch the nearest way . . . [1.5.16-18]

In other words, Macbeth is compassionate. He lacks the same ambition that she has. Even worse—at least to Lady Macbeth's way of thinking—he has a conscience!
When Macbeth is deciding whether or not to kill Duncan in his soliloquy at the beginning of Act 1, Scene 7, he consults with his conscience. He decides that his ambition is corrupting his sense of right and wrong and decides not to kill Duncan.

I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on the other. [1.7.25-28]

Macbeth ultimately feels guilty about killing Duncan:

Ere we will eat our meal in fear and sleep
In the affliction of these terrible dreams
That shake us nightly: better be with the dead,
Whom we, to gain our peace, have sent to peace,
Than on the torture of the mind to lie
In restless ecstasy. [3.3.20-25].

If Macbeth didn't have a conscience, he wouldn't feel guilty.