The Cocotron is an open source project which aims to implement a cross-platform Objective-C API which parallels Cocoa.
The project scope includes the AppKit, Foundation, Objective-C runtime and support APIs such as CoreGraphics and CoreFoundation. Projects for both OS X and Windows are build within Xcode—for the Windows version, frameworks are included as DLLs.
Interested parties should be aware that Cocotron is an open-source work in progress, and although some applications port well, strange things sometimes happen in the Windows runtime.
Here are several articles relating to Cocotron:
Anything new in Cocoa since 10.3 is less likely to be supported, and since some of the newest technologies are the coolest for Mac developers, Cocotron may not be as compelling as you might first suspect. In any case, don't let your perception of Cocoa or Objective-C be shaped by the quality of cross-platform efforts!