Shakespeare doesn't directly include an answer to this question in the text of Romeo and Juliet, but we can make some inferences:

Lady Capulet was not old enough to have had many children before Juliet: "I was your mother much upon these years" (Act 1, scene 3, line 78). This means that when she was Juliet's age, thirteen, Lady Capulet was already Juliet's mother. It would have been physically impossible for her to have had more than a couple of babies by the age of thirteen, so we know Juliet couldn't have had many older siblings, but it's possible Lady Capulet could have had more children after Juliet.

As cnorth points out, Lord Capulet had other children but they are all dead: "Earth hath swallowed all my hopes but she;" (Act 1, scene 2, line 14). We know that Lord Capulet is much older than his wife. In Act 1, scene 5, at the masquerade, Lord Capulet and his cousin work out that it has been thirty years since the two of them last "Were in a mask" (Act 1, scene 5, line 38), or were young bachelors seeking eligible young ladies to dance with. Since his wife is not even thirty years old, it is quite possible that Lord Capulet had another wife before Juliet's mother. It was not uncommon for infants to be still born or die shortly after birth in Shakespeare's day, and it was also quite common for young women to die in childbirth (especially since they were married and birthing children at such young ages!) So we can say it is possible that Lord Capulet had many children before Juliet. However, Juliet is his only LIVING child.

In Act 1, scene 3 the nurse discusses her deceased daughter, Susan, who was the same age as Juliet: "Susan and she (God rest all Christian souls!) / Were of an age. Well, Susan is with God;" (Act 1, scene 3, lines 20-21). This tells us that Juliet's wet nurse had a daughter who played with Juliet. However, since the nurse does not mention any other children, we can infer that the Capulets did not have any other children close to Juliet in age who survived long enough to play with their sister. When the nurse tells Juliet she was the prettiest baby she'd ever nursed, "Thou wast the prettiest babe that e’er I nursed," (Act 1, scene 3, line 65) we can infer that she has nursed other children before Juliet. It's possible that Juliet's nurse was employed by Capulet as a nursemaid since before Juliet came along, supporting the supposition that Capulet had other children before Juliet.

gbeatty is correct. They have had other children (we can assume 2 or more since they are refered as plural) but all have passed away.

Act 1, Scene 2, line 14 "The earth hath swallowed up all my hopes but she."

Great question!
Scholars don't know for sure. (See, for example, the article in Shakespeare Quarterly by Richard Hosley titled "How Many Children Did Lady Capulet Have?") All we know is that they are all dead now, according to Lord Capulet.