OriginalGriff's solution is very good, but maybe this one's more convenient and easier to understand for you:
When you click on a PictureBox the border is already set to Fixed3D because of the MouseHover event (btw. better is to use MouseEnter).
So if you want to permanently keep this type of border you can just unsubscribe from the MouseLeave event (you can restore the border mechanism with the right mouse button):
private void PictureBoxes_MouseClick(object sender, MouseEventArgs e)
{
PictureBox pBox = sender as PictureBox;
if (e.Button == MouseButtons.Left)
{
pBox.MouseLeave -= PictureBoxes_MouseLeave;
}
else if (e.Button == MouseButtons.Right)
{
pBox.MouseLeave -= PictureBoxes_MouseLeave;
pBox.MouseLeave += PictureBoxes_MouseLeave;
}
}