Windows XP (may work on Win2k or Vista, haven't tried)
A functional COM port - if you have only USB, you can order one from RetroFloppy
Updates:
2008-07-12: Published version 1.0.0.15 which includes:
Keyboard support - as you type on the Apple II client, keys are sent back to the Windows server. If the vnIIc window is not active, key events are sent to Windows. So you can, for example, type into Notepad.
Joystick/Paddle support - paddle states are sent to the Windows server as well. If the vnIIc window is not active, these are translated into mouse events.
Open/Closed Apple (a.k.a. Joystick/Paddle button) support - these are mapped to the left and right ALT keys. Sorry, you can't click the mouse with the Apple.
Screen region selection - click the "+" button at the top of the window, then drag your mouse to select part of your desktop to focus in on - great for streaming non-fullscreen applications.