I'm starting to learn Objective-C and I don't have a Mac (and I don't have plans to get one), but as I see that Cocoa is a very good framework to develop in Objective-C, I want to know: Is it possible to develop using Cocoa in Windows and Linux?
Thanks.
Take a look at Cocotron
The purpose of the project is to provide an easy to use cross-platform solution for Objective-C development. In particular, source code level compatibility with recent versions of Apple's frameworks (OS X 10.4 and 10.5).
The general goal is to provide complete support on any viable platform, the project is intended to be as portable as possible. However, most of the work at this time is focused on providing support for Microsoft Windows. In particular the NT based versions, 2000 up to Vista.
I think that your best bet, if you want to use Cocoa, is to get a Mac. You really won't regret it. GNUstep is a neat solution, but it is impractical to distribute applications built using GNUstep, because (as far as I know), clients must have the runtime installed for it to work.
Cocotron is an amazing project as well, and in the future, it may be useful for you if you want simple apps to run on both Mac OS and Windows. But you would still need a Mac to use it.
If you are interested in using a language like Objective-C with a framework like Cocoa, but don't want to get a Mac, why don't you try web application development with Cappuccino and Objective-J?. Objective-J is an implementation of an Objcective-C-like language in JavaScript, and Cappuccino is a really amazing imitation of the Cocoa framework in Objective-J.
Some examples of what can be created using that framework are 280 Slides and the new, stunningly beautiful EnStore. That's not a perfect solution, and unless you are content to just do web applications, you should buy a Mac.
Check out GnuStep.org.
You can also run Snow leopard Server inside a virtual machine, like VMWare Fusion. Apple changed it licence in 2008 to allow that, but only with server editions. I have personally used it with some success to deploy iphone applications (Although it was admitably a bit slow).
You will need decent hardware and preferably a dedicated hard-disk drive to be able to use it properly. And considering the cost of vmware and osx server you might be better off buying a used mac.