Solution 1:

Any Component can have a MouseListener. JLabel is nice for a colored rectangle, as long as you make it opaque.

Addendum: Having recommended MouseAdapter elsewhere, I should mention that one instance is enough.

Addendum: This update adds the mouse listener in the ColorLabel constructor.

ColorLabel picture

import java.awt.Color;
import java.awt.Dimension;
import java.awt.EventQueue;
import java.awt.GridLayout;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.util.Random;
import javax.swing.JFrame;
import javax.swing.JLabel;

/** @see http://stackoverflow.com/questions/5136859 */
public class ColorLabel extends JLabel {

    private static final int N = 10;
    private static final Random random = new Random();
    private static final MouseAdapter listener = new MouseAdapter() {

        @Override
        public void mousePressed(MouseEvent e) {
            ColorLabel label = (ColorLabel) e.getSource();
            label.setBackground(new Color(random.nextInt()));
        }
    };

    public ColorLabel() {
        this.setOpaque(true);
        this.setBackground(new Color(random.nextInt()));
        this.setPreferredSize(new Dimension(32, 32));
        this.addMouseListener(listener);
    }

    private void displayGrid() {
        JFrame f = new JFrame("ColorGrid");
        f.setLayout(new GridLayout(N, N));
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        for (int i = 0; i < N * N; i++) {
            final ColorLabel label = new ColorLabel();
            f.add(label);
        }
        f.pack();
        f.setLocationRelativeTo(null);
        f.setVisible(true);
    }

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

            @Override
            public void run() {
                new ColorLabel().displayGrid();
            }
        });
    }
}

Solution 2:

Instead of having a JPanel that you draw your grid of colors on, how about you have a grid of buttons. You override the drawing mechanism for the button so that it just renders as it's current color. Then you have functionality built in to listen for clicks to occur in a specific section of your grid.

Solution 3:

This is what I came up with. Note: I'm still studying Java in University, so this might not be the exact way to do this but it worked when I did it.

public class ColorGrid extends JPanel implements MouseListener {
this.addMouseListener(this);
addMouseListener(this);

That's the first part, the second part is to have these methods in your code.

public void mouseClicked(MouseEvent arg0) {

}

public void mouseEntered(MouseEvent arg0) {

}

public void mouseExited(MouseEvent arg0) {

}

public void mousePressed(MouseEvent arg0) {

}

public void mouseReleased(MouseEvent arg0) {

}

Then, depending on what you want, (i.e. Mouse clicked or pressed), just type in:

repaint();

Hope this helped.