No.  You only write the catch{} 
blocks for the exceptions you
wish to handle.
The other exceptions are passed up to the caller.
Exception handling is important for user-friendly programs. Here is the compute-the-square program again, this time written so that the user is prompted again if the input is bad:
import java.util.* ;
public class SquareUser 
{
  public static void main ( String[] a ) 
  {
    Scanner scan = new Scanner( System.in  );
    int num = 0 ;
    boolean goodData = false;
    while ( !goodData )
    {
      System.out.print("Enter an integer: ");
      try
      {
        num      = scan.nextInt();      
        goodData = true;
      } 
      catch (InputMismatchException  ex )
      { 
        System.out.println("You entered bad data." );
        System.out.println("Please try again.\n" );
        String flush = scan.next();
      }
    }
    System.out.println("The square of " + num + " is " + num*num );
  }
}
This is a common style for reading user input. It would be useful to copy, save, and run this program.
Could the following statement be moved into the try{} block?
System.out.println("Enter an integer:");