JTextAreaTableExample.java:

import javax.swing.border.*;
import javax.swing.event.*;
import javax.swing.table.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.*;
import java.awt.*;
  
public class JTextAreaTableExample extends JFrame {
 
  public JTextAreaTableExample() {
    super( "JTextAreaTableExample Example" );
  
    DefaultTableModel dtm = new DefaultTableModel() {
       // make first cell uneditable
       public boolean isCellEditable(int row, int column)
       {
          return !(column == 0);
       }
    };
 
    dtm.setDataVector(new Object[][]{{ "JTextArea1", "This is a testnon long linesn" },
                                     { "JTextArea2", "Hello, world!" }},
                      new Object[]{ "String","JTextArea"});
                     
    JTable table = new JTable(dtm);
    table.getColumn("JTextArea").setCellRenderer(new TextAreaRenderer());
    table.getColumn("JTextArea").setCellEditor(new TextAreaEditor());
 
    table.setRowHeight(80);
    JScrollPane scroll = new JScrollPane(table);
    getContentPane().add(scroll);
 
    setSize( 400, 250 );
    setVisible(true);
  }
 
  public static void main(String[] args) {
    JTextAreaTableExample frame = new JTextAreaTableExample();
    frame.addWindowListener(new WindowAdapter() {
      public void windowClosing(WindowEvent e) {
        System.exit(0);
      }
    });
  }
}
  
class TextAreaRenderer extends JScrollPane implements TableCellRenderer
{
   JTextArea textarea;
 
   public TextAreaRenderer() {
      textarea = new JTextArea();
      textarea.setLineWrap(true);
      textarea.setWrapStyleWord(true);
      textarea.setBorder(new TitledBorder("This is a JTextArea"));
      JPanel panel = new JPanel();
      panel.setLayout(new BorderLayout());
      panel.add(BorderLayout.WEST, new JLabel(new ImageIcon("TrafficRed.gif")));
      panel.add(BorderLayout.CENTER, textarea);
      getViewport().add(panel);
   }
 
   public Component getTableCellRendererComponent(JTable table, Object value,
                                  boolean isSelected, boolean hasFocus,
                                  int row, int column)
   {
      if (isSelected) {
         setForeground(table.getSelectionForeground());
         setBackground(table.getSelectionBackground());
         textarea.setForeground(table.getSelectionForeground());
         textarea.setBackground(table.getSelectionBackground());
      } else {
         setForeground(table.getForeground());
         setBackground(table.getBackground());
         textarea.setForeground(table.getForeground());
         textarea.setBackground(table.getBackground());
      }
 
      textarea.setText((String) value); 
      textarea.setCaretPosition(0);
      return this;
   }
}
 
class TextAreaEditor extends DefaultCellEditor {
   protected JScrollPane scrollpane;
   protected JTextArea textarea; 
 
   public TextAreaEditor() {
      super(new JCheckBox());
      scrollpane = new JScrollPane();
      textarea = new JTextArea();  
      textarea.setLineWrap(true);
      textarea.setWrapStyleWord(true);
      textarea.setBorder(new TitledBorder("This is a JTextArea"));
      JPanel panel = new JPanel();
      panel.setLayout(new BorderLayout());
      panel.add(BorderLayout.WEST, new JLabel(new ImageIcon("TrafficRed.gif")));
      panel.add(BorderLayout.CENTER, textarea);
      scrollpane.getViewport().add(panel);
   }
 
   public Component getTableCellEditorComponent(JTable table, Object value,
                                   boolean isSelected, int row, int column) {
      textarea.setText((String) value);
 
      return scrollpane;
   }
 
   public Object getCellEditorValue() {
      return textarea.getText();
   }
}

Image used: