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.