C#

private int x;
private int y;
private bool first = true;

void Form1_MouseMove(object sender, MouseEventArgs e)
{ 
   if (first)
   {
      x=e.X;
      y=e.Y;
      return;
   }
   int aX = x-e.X;
   int aY = y-e.Y;
   
   // I do not remeber if it shoud be + or -
   this.Location = new Point(this.Location.X-aX, this.Location.Y-aY);
   x = e.X;
   y = e.Y;
}

this.SetStyle(
            ControlStyles.UserPaint |
            ControlStyles.AllPaintingInWmPaint |
            ControlStyles.DoubleBuffer, true);

[DllImport("user32.dll")]
public static extern bool GetCursorPos(out Point pt);

private int x;
private int y;
private int aX;
private int aY;

[DllImport("user32.dll")]
static extern bool GetCursorPos(ref Point lpPoint);

public Form1()
{
    InitializeComponent();
}

private void timer1_Tick(object sender, EventArgs e)
{
    Point pt = new Point();
    GetCursorPos(ref pt);
    if (aX != pt.X || aY != pt.Y)
    {
        aX = (pt.X - x);
        aY = (pt.Y - y);

        this.Location = new Point(pt.X - aX, pt.Y - aY);
    }
    x = pt.X;
    y = pt.Y;

}

Location = System.Windows.Forms.Control.MousePosition;

        private int x;
        private int y;
        private int aX;
        private int aY;  
        
       

        public Form1()
        {
            InitializeComponent();  
        }  
        
        private void timer1_Tick(object sender, EventArgs e)
        { 
            Point pt = PointToClient(Control.MousePosition)); 
            if (aX != pt.X || aY != pt.Y)
            {
                aX = (pt.X - x);
                aY = (pt.Y - y);

                this.Location = new Point(pt.X - aX, pt.Y - aY);  
            } 
            x = pt.X;
            y = pt.Y; 
             
        }

If you do something like this you get a nasty oscillating effect. I'm not sure why?

private void timer1_Tick(object sender, EventArgs e)
{
    this.Location = PointToClient(Control.MousePosition);
}

window.Location=Control.MousePosition;

movingControl.Location=containingControl.PointToClient(Control.MousePosition);

bool catchme = false;

private void frmMain_MouseDown(object sender, MouseEventArgs e)
    {
    catchme = true;
    }

private void frmMain_MouseUp(object sender, MouseEventArgs e)
    {
    catchme = false;
    }

private void frmMain_MouseMove(object sender, MouseEventArgs e)
    {
    if (catchme)
        {
        Location = System.Windows.Forms.Control.MousePosition;
        }
    }