After trying various methods, I found one that is pretty simple and I'd
like to share it for any other poor souls who have to do the same
thing.  Sorry if my solution is not general enough.  I am using Java
5.0.

SHORTCOMINGS OF OTHER SOLUTIONS

http://www.codeguru.com/java/articles/305.shtml
Wernitz' code almost worked for me.  First I fixed the getFont() = null
problem by using UIManager.getDefaults().getFont("Table.font").  Then
when I added a row to my table the "row added" event fired and then it
tried to use getRowHeight(void), which is undefined in Wernitz' code
because it assumes all rows are the same height, which they are not.
The result is that the cells painted correctly but the entire table
height was based (I suppose) on the default row height and ended up
clipping most of the bottom rows.  His MultiLineTable.java code was so
confusing for me that I just didn't want to have to override yet
another method in another class to resolve the calls to getRowHeight().

http://archive.devx.com/java/free/articles/Kabutz07/Kabutz07-1.asp
Kabutz' solution really became my solution, although with a slight
modification (of course!)

MY SOLUTION

Below is the *only* class I needed to create.  I keep the original
author's comments for credit, but note that I changed it a bit by (1)
cleaning up some empty methods and unnecessary imports and deleting the
"implements Serializable", which JTable already implements, (2) by
modifying the constructor to get the JTextArea to behave as I wanted
(only break at newlines) and (3) modifying
getTableCellRendererComponent() by inserting a variation of Kabutz'
solution (after "setValue(value);").

The magic is to simply call
setDefaultRenderer(Object.class, new MultiLineCellRenderer());
against the JTable or JTable descendant. I called it in the
constructor.  I don't know what Kabutz was talking about coordinating
cell renderers for various columns.  The default renderer applies to
all columns, and I figured a default renderer that handled Objects (and
Object descendants) should be general enough to fit most people's
needs.  I don't know what happens with primitive types.
Setting the preferredHeight in the cell renderer is so much easier than
all the math that Wernitz was doing, and it WORKED for me!

/**
* MultiLineCellRenderer.java
*
* Created: Mon May 17 09:41:53 1999
*
* @author Thomas Wernitz, Da Vinci Communications Ltd
<thomas_wernitz@clear.net.nz>
*
* credit to Zafir Anjum for JTableEx and thanks to SUN for their
source code ;)
*/

package multiLineTable;

import javax.swing.*;
import javax.swing.table.TableCellRenderer;
import javax.swing.border.*;

import java.awt.Component;
import java.awt.Color;

public class MultiLineCellRenderer extends JTextArea implements
TableCellRenderer {
 protected static Border noFocusBorder;

 private Color unselectedForeground;
 private Color unselectedBackground;

 public MultiLineCellRenderer() {
   super();
   noFocusBorder = new EmptyBorder(1, 2, 1, 2);
   setLineWrap(false);
   setWrapStyleWord(false);
   setOpaque(true);
   setBorder(noFocusBorder);
 }

 public void setForeground(Color c) {
   super.setForeground(c);
   unselectedForeground = c;
 }

 public void setBackground(Color c) {
   super.setBackground(c);
   unselectedBackground = c;
 }

 public void updateUI() {
   super.updateUI();
   setForeground(null);
   setBackground(null);
 }

 public Component getTableCellRendererComponent(JTable table, Object
value,
                        boolean isSelected, boolean hasFocus,
                        int row, int column) {

   if (isSelected) {
     super.setForeground(table.getSelectionForeground());
     super.setBackground(table.getSelectionBackground());
   }
   else {
     super.setForeground((unselectedForeground != null) ?
unselectedForeground
             : table.getForeground());
     super.setBackground((unselectedBackground != null) ?
unselectedBackground
             : table.getBackground());
   }

   setFont(table.getFont());

   if (hasFocus) {
     setBorder( UIManager.getBorder("Table.focusCellHighlightBorder")
);
     if (table.isCellEditable(row, column)) {
    super.setForeground( UIManager.getColor("Table.focusCellForeground")
);
    super.setBackground( UIManager.getColor("Table.focusCellBackground")
);
     }
   } else {
     setBorder(noFocusBorder);
   }

   setValue(value);
    int rowHeight = (int)getPreferredSize().getHeight();
    if (table.getRowHeight() != rowHeight) table.setRowHeight(rowHeight);

   return this;
 }

 protected void setValue(Object value) {
   setText((value == null) ? "" : value.toString());
 }
}