public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();

            AddClipboardFormatListener(this.Handle);
        }

        protected override void WndProc(ref Message m)
        {
            if (m.Msg == WM_CLIPBOARDUPDATE)
            {
                Console.WriteLine("剪贴板内容改变");
            }
            base.WndProc(ref m);
        }

        //---------------------

        public const int WM_CLIPBOARDUPDATE = 0x031D;

        [DllImport("user32.dll", SetLastError = true)]
        public static extern bool AddClipboardFormatListener(IntPtr hWnd);
        [DllImport("user32.dll", SetLastError = true)]
        public static extern bool RemoveClipboardFormatListener(IntPtr hWnd);
    }

　　Form Close事件中再调用RemoveClipboardFormatListener：

RemoveClipboardFormatListener(this.Handle);