There is no official list, but when people speak of the four most famous, they almost always mean the tragedies Hamlet, Othello, King Lear, and Macbeth, which English Wikipedia highlights among the most celebrated. The Portuguese edition of Wikipedia also cites, beyond them, Romeo and Juliet and the comedy A Midsummer Night's Dream. Romeo and Juliet is the one that most often appears outside this group of four.
Each one entered these lists for a reason. Hamlet is Shakespeare's longest play, one of the most quoted works in the English language, and considered by many one of the greatest plays of all time; it tells of a prince who delays avenging his father. Romeo and Juliet was among the most popular of his plays even during his lifetime and, with Hamlet, is one of the most staged; it shows love taken over by haste. Othello deals with certainty manufactured by another's word, and Macbeth with ambition that, once satisfied, can only be sustained with more blood. Julius Caesar, another widely read tragedy, deals with political crime justified in the name of liberty.
Among the comedies, A Midsummer Night's Dream leads an index of productions announced by theater companies since 2012. It is a good reminder that fame in reading, on stage, and in school do not always coincide: the play most often staged is not necessarily the one most often cited.
On Clavis: Hamlet, Othello, Macbeth, Romeo and Juliet, Julius Caesar.