In short, Macbeth is a picture of human nature at its weakest and worst as well its finest--and human nature does not change. What Macbeth struggles with on this grand scale is something we all deal with on a generally much smaller scale. We are all tempted to want more than we should have or deserve, and sometimes we are willing to do something immoral or illegal to make that happen. We have been, as Banquo was, suspicious of our friends but want to believe the best of them, though people are generally not killed for having such suspicions. Some are willing to lose everything, as Macduff is, for the greater good. It's all part of the human condition.
The play also deals with the issue of fate and free agency. Does Macbeth really make his own decisions in this play or is he fated to act as he does? This issue comes up in many Shakespeare plays, with Macbeth and Romeo and Juiiet being the most obvious examples.
Macbeth deals with many universal themes:
1. The temptation that we all have to better ourselves in our career at the expense of others. Just as Macbeth it tempted to kill Duncan to advance his position, the temptation of "vaulting ambition" is prevalent in our cut-throat business practices.
2. What it means to be a man. The play defies machismo stereotypes and shows that a true man is not one who is ruthless and ambitious, like Macbeth, but one who is able and willing to sacrifice himself for the good of others, like Macduff.
3. The difficulty of judging others correctly. It shows how easily we can deceived by appearances, as was Duncan, and to some extent Banquo.
4. The devastating effects of guilt. Committing a crime has deep consequences on one's psyche and one's relationships with others.
5. The power struggles within a marriage, such as that as displayed between Macbeth and Lady Macbeth.