Apple - Is there an AirDrop client for Microsoft Windows?

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.

I install Pidgin on my Windows machines and enable its Bonjour account, which enables file transfers - including with Macs running iChat.

AirDrop is Lion-only, but iChat file transfer works 10.4+.

As other answers have said there's currently nothing for non-Apple OSes which can talk to Apple's AirDrop.

However there is Snapdrop which offers similar functionality to AirDrop via a cross-platform and open source web app. It does require the sending and receiving devices to be connected to the same LAN (rather than creating an ad-hoc wireless network like AirDrop) and uses WebRTC (with a fall back to WebSockets) for peer-to-peer communication directly between them.

More technical details about it can be found on the GitHub page.