Shakespeare's Plays Are Divided Into 4 Categories. What Are They?

You could actually say there are five categories.

Traditionally, Shakespeare's plays could be divided into three different categories; Comedies, Tragedies and Histories, in order of how many of each Shakespeare wrote, with the most first.

However, recently some have argued for a fourth category, Romances, which include The Tempest, Cymbeline, The Winter's Tale, The Two Noble Kinsmen and Pericles, Prince of Tyre (though Romeo and Juliet, Shakespeare's famous 'love story', remains a tragedy due to the nature of the ending).

Finally, some plays have become so notoriously difficult to categorise that they've been labelled Problem plays, rather aptly, which normally refers to three plays; All's Well That Ends Well, Measure For Measure and Troilus and Cressida, though some critics might extend this to The Winter's Tale, The Merchant Of Venice and Timon of Athens.

And there you have it. The four (or five) categories of Shakespeare's plays; Tragedies, Comedies, Histories, Romances and Problem Plays, the fifth category.

Comedies tragedies romances histories

Tragedy, eg romeo and Juliet, this is a tragedy because they both die, in fact, loads of them die in that play, and it has a sad ending.
Comedy, eg a midsummer nights dream, this is a comedy because the naughty fairies play tricks on the four lovers

He wrote primarily three types: Tragedy (Romeo and Juliet, as others have mentioned), comedy (Much Ado About Nothing, A Midsummer's Night's Dream, and more) and histories like Richard III.

He wrote lots of plays but they were categorised into 4 groups.

Histories
Comedies
Romances
Tragedies

There were also problem plays or tragicomedies

He wrote Romeo & Juliet and A mid Summer nights dreams

He wrote romeo & juliet I liked that movie because it was about love

Hamlet was also written by him between 1600 & 1602 & it is about a prince who want to avenge for his father.

Loads, for example some contained misfortune, and death, love, sorrow, some of the plays were called:
Macbeth, Romeo and Juliet, The tempest etc...

All sorts

This is just my thoughts, but I think that Shakespeare's's plays are divided into four different categories, which are tragedies, humor, history, and finally romances.

In the first officially published versions of Shakespeare's plays, known as The First Folio, the plays were categorised as Histories, Comedies and Tragedies.
 
Later critics have called some of the plays "Tragicomedies", "Romances" or "Problem Plays" because they do not readily fit into the original three categories.
 
In this context "Romance" is not the same as "Love Story."