What are some of the major events that cause Macbeth's downfall?

First, and most obviously, he believes the Weird Sisters.  Despite Banquo's warnings that they might not be telling him the truth, Macbeth whole-heartedly believes their prophecies to be fact. This inflames his ambition and desire for power.

As a result, he kills Duncan.  Despite his very many reasons not to kill him -- Duncan is his relative, his friend, his king, his guest, and just all around a really good guy -- he had only...

First, and most obviously, he believes the Weird Sisters.  Despite Banquo's warnings that they might not be telling him the truth, Macbeth whole-heartedly believes their prophecies to be fact. This inflames his ambition and desire for power.

As a result, he kills Duncan.  Despite his very many reasons not to kill him -- Duncan is his relative, his friend, his king, his guest, and just all around a really good guy -- he had only one reason to go ahead, and that was his ambition.  When Lady Macbeth wounds his pride by insisting that he is not a man if he will not go through with it, she seals the deal.

Later, although Macbeth has attained the position he wanted, he now has to work to hold onto it.  He fears that Banquo's family will somehow take his throne from him because the Weird Sisters said that Banquo would father kings (and so Macbeth interprets this to mean that he will not pass on his crown to his own heirs).  Thus, Macbeth arranges the murders of Banquo and Fleance, though Fleance escapes.

At this point, Macbeth tells his wife, "Blood will have blood" and "We are yet but young in deed" (3.4.151, 176).  He means that now that they have committed one murder (two for him), they will have to keep going; there are still many more people they will need to get rid of if they want to feel secure in their positions.

When next he goes to see the Weird Sisters for more information, he again believes everything he sees and hears, despite having little reason to trust them.  Hecate said that she would raise "artificial sprites" designed to make Macbeth feel more secure than he really is, and so he will let down his guard.  He naively believes everything he hears and becomes overconfident.

In the end, Macbeth's credulousness (in terms of believing everything the sisters tell him), his ambition and pride (the two qualities that compel him to murder Duncan), and his ultimate willingness to do and kill whomever is necessary, lead to his downfall.