Although there are many examples of the various forms of conflict apparent in Shakespeare's Macbeth (even man vs the supernatural or God), there are a long list of examples of man vs man as well.
Quite literally, there is the battle that Duncan and his men are involved in as the play begins. When Macbeth and Lady Macbeth argue about killing Duncan, this is man vs man. Of course, other examples would begin with Macbeth's murder of Duncan, the murderers killing Banquo, and Macbeth's men killing Macduff's family.
An interesting example of this conflict is also seen when Macduff approaches Malcolm, Duncan's son (who fled to England when his father was murdered). In this scene, Malcolm does not trust Macduff as he is a member of Macbeth's court, and Malcolm (rightful heir to the Scottish throne) wrongly suspects that Macduff may be in league with Macbeth, having come to England to kill him. When word arrives regarding the slaughter of Macduff's family, Malcolm realizes Macduff has sacrificed all to be there in an effort to save Scotland from the tyrant Macbeth.
There is conflict toward the end of the play, of course, when Macbeth kills young Siward in battle. Over his dead body, Macbeth boasts (foolishly still believing the witches' misleading predictions) that the young man died because he "was born of a woman" and Macbeth fears no man.
Thou wast born of woman.
But swords I smile at, weapons laugh to scorn,
Brandish'd by man that's of a woman born. (V.vii.15-17)
Ultimately, Macbeth faces a vengeful Macduff, believing that Macduff cannot defeat him. Telling Macduff he is wasting his time in trying to defeat a "charmed" Macbeth, he declares that anyone born of a woman (every one) cannot kill Macbeth. To Macduff, the villainous Macbeth says:
Thou losest labor.
As easy mayst thou the intrenchant air
With thy keen sword impress as make me bleed:
Let fall thy blade on vulnerable crests;
I bear a charmed life, which must not yield
To one of woman born. (V.viii.12-16)
However, Macduff attacks Macbeth advising him to tell the evil beings he serves that Macduff was not "born" in the traditional way, but through Caesarian section.
Despair thy charm,
And let the angel whom thou still hast served
Tell thee, Macduff was from his mother's womb
Untimely ripp'd. (lines 17-20)
Macduff then kills Macbeth in battle. There are other examples, but this includes the highlights.