Is there an AirDrop client for Microsoft Windows? It would be nice to have an AirDrop client for Microsoft Windows. Does anyone know if such a program exists as a shipping product or an open source work-in-progress?

I'm aware that there are many other file sync options, but I'm looking for something that works with Apple's implementation from the Windows OS.
No, I don't believe you can. Apple advertise AirDrop as: "AirDrop, a remarkably simple way to copy files wirelessly from one Mac to another with no setup;"
.
Key part of that sentence being "from one Mac to another" - Second bullet point: http://www.apple.com/uk/pr/library/2011/02/24Apple-Releases-Developer-Preview-of-Mac-OS-X-Lion.html. It's highly unlikely Apple would open this feature up to Windows or Linux because it's a selling point for them in new Macs running Lion.