.NET hide titlebar but keep border

Set FormBorderStyle to FormBorderStyle.Sizable or FormBorderStyle.SizableToolWindow and set Text to an empty string, and ControlBox to false

Note that FixedToolWindow won't work, it will remove the border. If you don't want it to be sizable, use SizableToolWindow and add this to the form's codebehind (adding both languages since you don't specify and tagged the question with both):

In vb.net:

Protected Overrides Sub WndProc(ByRef message As Message)               
    If message.Msg = &H84 Then ' WM_NCHITTEST
        message.Result = CType(1, IntPtr)
        Return
    End If    
    MyBase.WndProc(message)
End Sub

In C#:

protected override void WndProc(ref Message message)
{
    if (message.Msg == 0x0084) // WM_NCHITTEST
        message.Result = (IntPtr)1;   
    else base.WndProc(ref message);
}