Why won't the loop stop iterating?

Question 1

First of all, your code iterates through a board and generates random marks of X and O. This leads to some very odd board states, being always filled row-by-row, and possibly with unbalanced number of X and O marks.

IMHO you should organize your code in opposite manner to fill a board similary to a true game. I mean a series of 9 marks 'XOXOXOXOX' spreaded over the board.

Let Labels labels be a nine-character array, initialized to 9 spaces.

public int doGame( Labels labels)
{
    labels = "         ";
    int itisXmove = true;              // player X or O turn
    for( int movesLeft = 9; movesLeft > 0; movesLeft --)
    {
        int position =          // 0 .. movesLeft-1
                (int) Math.floor(Math.random() * movesLeft);

        for( int pos = 0; pos < 9; pos ++)        // find position
            if( labels[ pos] == " ")              // unused pos?
                if( position-- == 0)              // countdown
                {
                    if( itisXmove)                // use the pos
                        labels[ pos] = "X";       // for current player
                    else
                        labels[ pos] = "O";
                    break;
                }

        int result = checkWinner( labels);        // who wins (non-zero)?
        if( result != 0)
            return result;

        itisXmove = ! itisXmove;                  // next turn
    }
    return 0;                                     // a tie
}

then

public void actionPerformed(ActionEvent e)
{
    Labels labels;

    int result = doGame( labels);

    if( result == valueForX)
        JOptionPane.showMessageDialog(null, "X is the Winner!");
    else if( result == valueForO)
        JOptionPane.showMessageDialog(null, "O is the Winner!");
    else
        JOptionPane.showMessageDialog(null, "It's a tie!");

    for( int rowpos = 0; rowpos < 9; rowpos += 3)
    {
        for( int colpos = 0; colpos < 3; colpos ++)
            /* output (char)label[ rowpos + colpos] */;

        /* output (char)newline */;
    }
}

Question 2

The easiest way would be to break all loops at once. (Even if some people dont like this)

outerwhile: while(true){

  // Generate random # 0-1 for the labels and assign 
  // X for a 0 value and O for a 1 value

  for (int row = 0; row < gameboard.length; row++) //rows
  {
    for (int col = 0; col < gameboard[row].length; col++) //columns
    { 

      total = checkWinner(gameboard);     
      if(total == 30 || total == 300)        
        break outerwhile;  //leave outer while, implicit canceling all inner fors.


      i++; //next label
    }
  }//end for
}//end while

This However would not allow for the "tie" option, because the while will basically restart a game, if no winner has been found. To allow tie, you dont need the outer while at all, and can leave both fors at once, when a winner is found:

  Boolean winner = false;
  outerfor: for (int row = 0; row < gameboard.length; row++) //rows
  {
    for (int col = 0; col < gameboard[row].length; col++) //columns
    { 

      total = checkWinner(gameboard);     
      if(total == 30 || total == 300){        
        winner = true;     
        break outerfor;  //leave outer for, implicit canceling inner for.

      }

      i++; //next label
    }
  }//end for

  if (winner){
    //winner
  }else{
     //tie.
  }

Question 3

I think you should change your loop condition and add one more bool.

You have a "tie" condition but currently you only check for winner. The only explanation without the checkWinner code is that you are encountering a tie every time.

So...

boolean tie;
boolean winner;

do {
//your stuff
}
while(!(tie || winner))

Edit: I didn't realize you put the while loop outside your for loop, you will need to break out of your for loops in order for the while condition to be checked.

//stop current game if a winner is found
    do{

      for (int row = 0; row < gameboard.length; row++) //rows
      {
        for (int col = 0; col < gameboard[row].length; col++) //columns
        { 
            if(winner || tie)
                break;
        }//end for

        if(winner || tie)
            break;
      }//end for
    }while(!(winner || tie));//end while
//the rest of your stuff here

Question 4

You're not checking the value of winner until both for loops complete. Add a break right after you set winner = true, and add an

if (winner)
{
    break;
}

to the beginning or end of your outer for loop.

Question 5

Your issue is that your do/while statement is wrapped around the for statements. So the for statements end up running their entire cycle before it ever reaches the while statement. A solution to get around this is checking for a winner in the for statements and breaking:

//stop current game if a winner is found
do {

    for (int row = 0; row < gameboard.length; row++) //rows
    {
        for (int col = 0; col < gameboard[row].length; col++) //columns
        { 

            // ... your other code ...

            total = checkWinner(gameboard);
            if(total == 30 || total == 300) {
                winner = true;
                break; // end current for-loop
            }

            i++; //next label
        }

        if (winner) break; // we have a winner so we want to kill the for-loop
    } //end for

} while(!winner); //end while

So you should be able to just loop through the two for-statements and break upon a winner. Your code also does not seem to handle a tied case, but I am guessing you already know that.