It is possible to "cut" off a form pieces of variuos shape using API functions:

CreateEllipticRgn
CreateRectRgn
CombineRgn
SetWindowRgn
DeleteObject
GetSystemMetrics

And still mouse can be used to move such form, event if with its titlebar and caption not available. Win API functions:

ReleaseCapture
SendMessage

Here is some examples (members area, alas):

How to create a round form
http://www.news2news.com/vfp/?example=143

How to create a transparent area in a form
http://www.news2news.com/vfp/?example=126&function=174

How to Move a Form not using its Titlebar or Caption
http://www.news2news.com/vfp/?example=195&function=313