What are some modern day examples of Macbeth?

I think there are many individuals who would characterize the current president of the United States, Donald J. Trump, as a modern-day Macbeth.

1. He was a political outsider before he came to power. Unlike the rest of the Republican field of candidates and the two Democratic candidates for the Oval Office, Trump had no congressional or governmental experience prior to his candidacy and subsequent election. Likewise, no one would have considered Macbeth as a possible king prior to Duncan's murder. When Duncan was alive, he'd named his older son, Malcolm, as his heir, and he even had a younger son, Donalbain, who would be in line for the throne before Macbeth (who was a more distant relative).

2. The Trump administration has also been responsible for the departure—whether it was voluntary or the person was fired—of many government officials such as U. Attorney General Sally Yates, Chief Strategist Steve Bannon, and FBI Director James Comey, to name a few. Just as many of the thanes who were once loyal to Macbeth, like Macduff or Ross or Lennox, eventually turned on him, so many of Trump's former friends and associates have been eliminated from or have chosen to leave his administration.

3. Trump has also adopted policies which many view as dangerous to both the United States and the world, just as Macbeth kind of ran Scotland into the ground. Trump has gotten rid of environmental protections that will likely lead to dangerous changes in the environment in coming years, and he seems to be interested in isolating the US from much of the rest of the world (by building border walls, removing the country from international deals made by past administrations, etc.).

Obviously not all Americans would characterize President Trump in this way, but evidence is certainly available should you want to make the case.

In some ways Richard Nixon is a Macbeth because he wished to eliminate his enemies before he became president in his second term (Watergate Scandal), and he became paranoiac.  A tragic figure, Nixon was a good ruler with a successful first term; however, his "vaulting ambition" led to his seizing greater executive power.  After his resignation, some of this executive privilege was removed. 

Anyone who does an evil deed for personal gain could be considered a modern-day Macbeth. This would be especially true if the evil deed was influenced by outside sources (like the witches and Lady Macbeth in the play).  Bernie Madoff and his scheme to embezzle from investors comes to mind.

It's hard to think of anyone who fits Macbeth's exact profile, although Hitler, Stalin, and Idi Amin have been suggested in previous answers to a similar question (see link below).  Among very recent figures, I know that some people would compare Macbeth to George W. Bush for the following reasons:

1. They would claim that he came to power illegitmately, in the 2000 election.

2. They would claim that he felt as if he almost deserved the job of president, or was destined for it, because his father had been president.

3. They would claim that he did great evil during his presidency.

4. They would say that by the end of his term of office his presidency had essentially collapsed and that he wasn't sure what to do in response.

5. They would say that by the end of his term he had won the contempt and hatred of many people.

6. They would say that he was replaced by a far better figure.

I do not mean to indicate at all that I personally think that George W. Bush was comparable to Macbeth, but surely there are many people who would see similarites between the two. Still, it is hard to think of Laura Bush as in any way comparable to Lady Macbeth.  Bush's critics would probably cast Dick Cheny in that role.

http://www.enotes.com/macbeth/q-and-a/macbeth-similar-what-3-historical-figures-would-178169

What are some modern examples that demonstrate Macbeth's relevance today?

Just look at any state-induced acts of terrorism sponsored by a totalitarian government.  Just as Macbeth has his political enemies murdered (Banquo, Macduff's wife and child), so too have despots killed and taken hostage political enemies of the state.  Macbeth does not commit the murders himself, but he sponsors them.  Most political "hits" are managed the same way.  Macbeth represents a very modern, Machiavellian leader: vindictive, violent, controlling, and paranoid.

Look at how some of the descriptions of the following despots and autocrats:

Vladimir Putin: "As president he gained a reputation as a clever and ruthless political operator with a hunger for Russian power and not too much concern for the niceties of democracy or diplomacy."

Kim Jong-il: "the North Korean system became even more centralized and autocratic under Kim Jong-il than it had been under his father. Although Kim Il-sung required his ministers to be loyal to him, he nonetheless sought their advice in decision-making; Kim Jong-il demands absolute obedience and agreement, and views any deviation from his thinking as a sign of disloyalty. According to Hwang, Kim Jong-il personally directs even minor details of state affairs, such as the size of houses for party secretaries and the delivery of gifts to his subordinates."

Saddam Hussein: "On 5 November 2006, he was convicted of charges related to the 1982 killing of 148 Iraqi Shi'ites convicted of planning an assassination attempt against him, and was sentenced to death by hanging."