stood,
As two spent swimmers that do cling together
And choke their art. The merciless Macdonwald—
Worthy to be a rebel…from the western isles
Of kerns and gallowglasses is supplied;
…but all's too weak;
For brave Macbeth—well he deserves that name—
Disdaining fortune, with his brandish'd steel,
…Like valor's minion carved out his passage
Till he faced the slave…
Till he unseam'd him from the nave to the chaps…
DUNCAN:
O valiant cousin! Worthy gentleman! (I.ii.9-26)

When Romeo "crashes" Capulet's party (and he is unwelcome, as a Montague), Tybalt wants to throw him out, but Capulet stops him, saying that he seems a decent man who is well-liked—that Typbalt should leave him alone.

TYB:
Uncle, this is a Montague, our foe;
A villain, that is hither come in spite
To scorn at our solemnity this night.
CAP:
Young Romeo is it?...
...Content thee, gentle coz, let him alone.
He bears him like a portly gentleman,
And, to say truth, Verona brags of him
To be a virtuous and well-govern'd youth. (I.v.63-71)

Romeo and Macbeth are very different, and in this regard, we see the goodness of Romeo and the evil rooted out in Macbeth.

Romeo is inexperienced. At first, he's infatuated with Rosaline and laments her disinterest. He is naive. On the other hand, Macbeth's only softness is shown in Act One, scene five, where he greets his wife in a letter as: “…my dearest partner of greatness..." (9-10). Later he calls her: My dearest love... (61). The next time the couple speaks, there is no love expressed. She insults him—his manhood, and his bravery; she tries her best to emasculate him so he will kill the king (making her queen), and he crumbles. Macbeth, a valiant warrior, allows her words to drive him to murder because his ambition is so great.

Macbeth is a fighter, and soon kills many people. Romeo is not a fighter at all. He is not involved in the feud between the Capulets and Montagues. He tries to interfere when Tybalt and Mercutio fight—and only lifts a sword to avenge Mercutio's death—carried out unethically by Tybalt.

Romeo falls in love with Juliet, and his life is changed forever. She is the center of his universe:

ROM:
…But soft! What light through yonder window breaks?
It is the East, and Juliet is the sun! (II.ii.2-3)

However, Macbeth admits that his ambition drives him to evil—for him, taking the throne means everything:

MACBETH:
…I have no spur(25)
To prick the sides of my intent, but only
Vaulting ambition... (I.vii.25-27)

Romeo and Macbeth are vaguely similar and very different.

Additional Source:

http://www.enotes.com/macbeth/summary

Hamlet and Macbeth are both obsessed with death. They are both nobles. Both are doomed to be tragic heroes.  They are different in many ways, though.  Hamlet is younger, and he’s not married.  He grapples with fears about questions about death, and Macbeth is obsessed with his own death.

The irony here is that because the names of the characters are identical to the names of the plays that contain those very characters, it's impossible for us to figure out whether you are talking about Hamlet/Macbeth the characters or Hamlet/Macbeth the plays.  Because you did not italicize the names, however, it leads me to believe you are referring to the characters.

I know this is probably going to sound obvious, but it's really important to bring up that both of these characters are two of Shakespeare's most famous tragic heroes.  The fact they are tragic heroes is a VERY important similarity!

As such (and to put the qualities of a tragic hero into one sentence), they are honorable men led to their deaths by a tragic flaw that they realize far too late.  Yes, these two characters have completely different tragic flaws:  Macbeth's is "vaulting ambition" while Hamlet's (whose tragic flaw is much more debatable) is often explained as inaction/intelligence (i.e. thinking too much).

In Macbeth and Hamlet, there are two women who agree to the destruction of another in order to make their lives more powerful. Both women, Lady Macbeth and Gertrude, are involved in plots to kill innocent kings. While it never directly states that Gertrude wanted Claudius to kill her husband Hamlet, she obviously wanted to marry him; otherwise she would not have married him. She so desired position and staus so she married him in a hurry.

Lady Macbeth is deliberate in her desire to see her husband crowned king of Scotland. She desires the power and prestige of being Queen of Scotland.

Both women are living with a horrible secret. If Gertrude does not know that Claudius killed her son's father, she does marry him knowing Claudius is her son's uncle.

The similarities between these two women are their desires for status and prestige. Both women are living with murderers. Both women desire to be powerful.

Both women die during each husband's term of being king.

There is a deeper connection between these two women. There husbands are guilty of murdering kings in order to take over the position of kingship.

The question is whether or not both women were in on the plot to murder the kings.

The two plays are tragedies, the principal characters both have close encounters with the supernatural.  For Hamlet, the ghost of his father tries to hell him the story of his murder, for Macbeth, the ghost of Banquo just haunts Macbeth with guilt.

Macbeth, a man so full of ambition, that he kills and kills is compared to Hamlet who has no ambition, he struggles to act on his father's murder.  Both characters end up thinking too much, although Macbeth is more action oriented than Hamlet, they both suffer from degrees of madness. 

 There are many similarities and differences between these two plays. In fact, since there are so many of both, we'll start with the basics.Ways they are similar:They deal with royalty.They deal with treachery.They deal with violence, and are marked by numerous deaths.The personal passions of the main characters are tied up with the fates of their nations.There are multi-generational issues and passions involved.Both have supernatural elements. Both have ghosts.  Ways they are different:Hamlet is single and isolated; Macbeth is married and part of a team.Hamlet is indecisive. Macbeth decides—he kills—but must change his plan as things develop.Macbeth must deal with a personalized and confusing prophecy.Hamlet is acted on; Macbeth acts.  

Numerous similarities exist between Shakespeare's Claudius and Macbeth.  Both are extremely ambitious.  So much so that they both assassinate a reigning monarch to achieve the throne for themselves.  Both also, when it becomes necessary, are willing to continue killing to maintain their power.  Both show the possibilities of scruples that make them question their own evil actions, although their sincerity is questionable; both may question or feel sorry for what they do/have done because they are worried about the consequences rather than because what they are going to do/have done is wrong. 

At the same time, Claudius is more intelligent than Macbeth.  Claudius does his own planning, and does it pretty well.  Claudius would get away with his assassination if not for the intervention of a ghost, an intervention he couldn't possibly have accounted for.  Macbeth needs lady Macbeth to do his planning for him.  His evil deeds are discovered once he starts planning his own murders, not when his wife plans a murder for him.  Macbeth is also the protagonist of his play and a tragic figure with a tragic flaw, while Claudius is an antagonist and is not a tragic figure.

Lady Macbeth and Claudius are similar in the fact that they both are, primarily, overly ambitious and would not allow anything to stand in their way to achieve their goals. Secondly, they are both murderers since both committed regicide. Lady Macbeth assisted in the assassination of King Duncan whilst Claudius murdered his own brother, King Hamlet. Both killed their victims whilst they were sound asleep. Both killed a relative - Lady Macbeth was related to Duncan through her husband, and Claudius committed fratricide.

The only difference in these heinous acts was that Lady Macbeth was complicit with her husband, whilst Claudius seemingly acted alone (although Hamlet believes that his mother may have been involved). The two were also similar in that they were both devious, putting on 'false faces.' Lady Macbeth even advised Macbeth to, 'look like the innocent flower, but be the serpent under't,' whilst Claudius acted as if he was Hamlet's caring, loving father, when he was actually planning his murder when he plotted with Rosencrantz and Guildenstern to lead Hamlet to his doom. Once they had committed their crimes, both did not display any immediate regret or remorse for their evil.

The major difference between these two villains is the fact that Lady Macbeth was overwhelmed with guilt later, so much so, that she would sleepwalk and rub her hands, trying to remove the blood on her hands, which she believed was impossible to wash off. She was constantly ranting about the terrible crime that she had committed. She was so overwhelmingly distraught that she later committed suicide. Claudius, on the other hand, neither expressed nor displayed any such remorse.

Unlike Lady Macbeth who wanted to bring an end to her torment, Claudius continued to plot murder. When Hamlet thwarted his plan to have him executed by the king of England, as per his instruction, he plotted with Laertes to kill Hamlet. He did this by acting as if he was assisting Laertes to avenge his father's death at Hamlet's hand, but he wanted desperately to kill the young prince who had been openly displaying his suspicion and mistrust. Hamlet became a threat and had to be removed.

It is indeed tragic that the selfish actions of these two pernicious felons resulted in the deaths of so many innocents.