Can I run OSX applications?

Solution 1:

Recently featured on Slashdot was the Darling project, which aims to provide Darwin / OS X emulation and can already run some Mac OS X applications on Linux.

It appears to be developed for academic purposes and is still in its early stages, but it looks promising. It is based on the aforementioned GNUstep.

Solution 2:

Sadly not.

There are various projects that attempt PowerPC emulation, but none that would allow you run your standard Mac OS X application.

Solution 3:

GNUstep as an equalivelent API to Cocoa, the NeXTstep based Mac API, but it's not complete, needs recompilation, and then your Mac app looks like it went back in time.

Solution 4:

There was a project attempting to do this for very old Mac Software (68k) called Executor: http://en.wikipedia.org/wiki/Executor_%28software%29 -- it is, of course, defunct.

There is no modern equivalent as far as I can tell, and making such a thing would be almost as big a task as Wine itself.

Solution 5:

EDIT: Reading the other answers, it appears that there are now ways to do what OP asked. I'm leaving this answer here because it is still a viable alternative on some hardware for applications which won't run under emulation.

While the other answers are correct (no, you cannot), there is a way to install OSX on Virtualisation software such as VirtualBox. This is not what you asked for, so be careful, but it may get you the results you need.

http://www.taranfx.com/install-snow-leopard-virtualbox