Using setValueAt to recreate mutually exclusive check boxes

Don't add your own MouseListener. Instead override setValueAt() in the TableModel to see the new value set by the default editor for Boolean.class.

Addendum: Here's an sscce. For expedience, it simply clears all entries in CHECK_COL, sets the new value and conditions the button accordingly.

import java.awt.*;
import javax.swing.*;
import javax.swing.table.DefaultTableModel;

/**
 * @see http://stackoverflow.com/questions/7920068
 * @see http://stackoverflow.com/questions/4526779
 */
public class CheckOne extends JPanel {

    private static final int CHECK_COL = 1;
    private static final Object[][] DATA = {
        {"One", Boolean.FALSE}, {"Two", Boolean.FALSE},
        {"Three", Boolean.FALSE}, {"Four", Boolean.FALSE},
        {"Five", Boolean.FALSE}, {"Six", Boolean.FALSE},
        {"Seven", Boolean.FALSE}, {"Eight", Boolean.FALSE},
        {"Nine", Boolean.FALSE}, {"Ten", Boolean.FALSE}};
    private static final String[] COLUMNS = {"Number", "CheckBox"};
    private DataModel dataModel = new DataModel(DATA, COLUMNS);
    private JTable table = new JTable(dataModel);
    private ControlPanel cp = new ControlPanel();

    public CheckOne() {
        super(new BorderLayout());
        this.add(new JScrollPane(table));
        this.add(cp, BorderLayout.SOUTH);
        table.setSelectionMode(ListSelectionModel.SINGLE_SELECTION);
        table.setPreferredScrollableViewportSize(new Dimension(250, 175));
    }

    private class DataModel extends DefaultTableModel {

        public DataModel(Object[][] data, Object[] columnNames) {
            super(data, columnNames);
        }

        @Override
        public void setValueAt(Object aValue, int row, int col) {
            if (col == CHECK_COL) {
                for (int r = 0; r < getRowCount(); r++) {
                    super.setValueAt(false, r, CHECK_COL);
                }
            }
            super.setValueAt(aValue, row, col);
            cp.button.setEnabled(any());
        }

        private boolean any() {
            boolean result = false;
            for (int r = 0; r < getRowCount(); r++) {
                Boolean b = (Boolean) getValueAt(r, CHECK_COL);
                result |= b;
            }
            return result;
        }

        @Override
        public Class<?> getColumnClass(int col) {
            if (col == CHECK_COL) {
                return getValueAt(0, CHECK_COL).getClass();
            }
            return super.getColumnClass(col);
        }

        @Override
        public boolean isCellEditable(int row, int col) {
            return col == CHECK_COL;
        }
    }

    private class ControlPanel extends JPanel {

        JButton button = new JButton("Button");

        public ControlPanel() {
            button.setEnabled(false);
            this.add(new JLabel("Selection:"));
            this.add(button);
        }
    }

    private static void createAndShowUI() {
        JFrame frame = new JFrame("CheckOne");
        frame.add(new CheckOne());
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.pack();
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }

    public static void main(String[] args) {
        java.awt.EventQueue.invokeLater(new Runnable() {

            @Override
            public void run() {
                createAndShowUI();
            }
        });
    }
}