Any Way to run Mac OSX software under Windows?

In short, no.

There is a project to run Mac binaries on Windows, but when I found it, about a year ago, it was a long way from reliably running simple Mach-O binaries, let alone emulating all the frameworks most GUI applications require (Cocoa, CoreImage and the likes).. I don't recall the name of the project, and it didn't seem very active at the time

There is Cocotron, "an open source project which aims to implement a cross-platform Objective-C API similar to that described by Apple Inc.'s Cocoa documentation" - but I don't think this is what you're after..

Again, no, there is nothing like WINE for running Mac software on Windows, and really I doubt there ever will be.

The closest you'll likely get is software being ported (via recompilation, which will involve a lot of modification to the source code), and as John T says, there's plenty of equivalent software which will be far better integrated with Windows..

To date there really is no application which does this well, although I'm sure there have been a lot of attempts. Your best bet is to find alternative software. Most software nowadays has a counterpart which does pretty much the same thing on a different operating system.

There's PearPC, which operates and acts as a virtual machine of sorts. This will allow you to install OS X in it's own environment and then run that from inside windows. I believe it's all about powerPC emulation so you may be limited to older versions of OS X... like Tiger and earlier. PearPC

Then there's the OSX86 (Hackintosh) route. This is where you grab one of the OSX installation disk images online which have been modified to install on intel & amd PC's. This is the route I chose. I'm running a Dell Vostro 1500 notebook with dual boot installations of OSX Snow Leopard & Windows 7 Ultimate. I love it and would actually consider OSX to be my main OS on this system. InsanelyMac