The Mouse Cursor Suddenly Has a Mind of Its Own

It could be a malfunctioning mouse.
Unplug the mouse (or turn it off, if it's wireless).  Is it still happening?
If so, do you have two pointing devices connected (touchpad? Thinkpad trackpoint?)
If not, try cleaning the crud from the bottom of the mouse, or changing the battery, or banging it on your desk, or (better yet!) replacing it.

Perhaps you let a scammer talk you into installng remote access software on your computer.
Do the mouse motions and clicks seem purposeful?
Disconnect the Internet. Is it still happening?
If disconnecting the internet prevents it from happening, then that's probably what's going on, especially if the mouse motions and clicks seem purposeful.
Quickest fix might be a System Restore to before it started happening, if you have restore points enabled. Before doing the system restore, be sure to save any important documents or pictures that you left on the Windows Desktop. System Restore should not change your Documents, Pictures & Downloads folders, but it WILL delete recent files form your Desktop.