William Shakespeare, the Bard, was an extremely prolific playwright during his time.  He wrote comedies, tragedies, and histories--37 plays total.  I organized his plays into genres for you, so you can see exactly how many he wrote in each genre and the titles.

Comedies:  Shakespearian comedies' primary purpose was humor and usually involved the antics of unmarried characters who usually end up happily married at the end of the play.

1. Love's Labour Lost
2. Much Ado About Nothing
3. Taming of the Shrew
4. Merry Wives of Windsor
5. Twelfth Night
6. All's Well that Ends Well
7. A Midsummer Night's Dream
8. Measure for Measure
9. Two Gentlemen of Verona
10. As You Like It
11. Winter's Tale
12. Tempest
13. Merchant of Venice
14. Comedy of Errors

Tragedies-- Shakespeare's tragedies involved a hero with admirable qualities, but some sort of tragic flaw.

1. Romeo and Juliet
2. Macbeth
3. King Lear
4. Hamlet
5. Titus Andronicus
6. Julius Caesar
7. Anthony and Cleopatra
8. Othello
9. Troilus and Cressida *sometimes considered a dark comedy
10. Coriolanus
11. Timon of Athens
12. Cymbeline *sometimes considered a dark comedy
    

Histories-- The Histories mostly focus on English history, with the exception of Pericles. 

1. Henry IV, Part I
2. Henry IV, Part II
3. Henry V
4. Henry VI, Part I
5. Henry VI, Part II
6. Henry VI, Part III
7. Henry VIII
8. Richard II
9. Richard III
10. Pericles *Not included in the First Folio, but later attributed to Shakespeare, also could be considered dark comedy
11. King John

Some also attribute Edward III to Shakespeare as well; if you included Edward III, the total number of works would be 38, but common consensus in most lists of Shakespeare's works by authoritative sources list his works as numbering 37.

Sources:

"Shakespeare's Collective Works". MIT. web. 15 Jun. 2012.

Shakespeare, William.  Complete Works of William Shakespeare. New York: Olympic, 1994.