There is no easy way to do this using standard UI controls. AppKit and UIKit are completely different animals. Even the basic UIView and NSView are very different in structure and function. At that level, you won't see anything that could be made cross-platform.
However, there are display elements that can be made to work on Mac and iOS with minimal changes. Core Animation CALayers are one such element, in that they are the same on Mac OS X and iOS. This is why we chose to use them as the basis for the Core Plot framework, which uses an almost identical codebase to display graphs on Mac and iOS. There are a few platform-specific things to tweak (like the inverted coordinate system a UIView applies to its backing layer), but most of the code will translate to both platforms.
You mention writing a game. If you are using OpenGL ES for this, much of the rendering code you write will also work on the Mac. There are a few things you will need to alter, but for the most part OpenGL ES is a subset of desktop OpenGL. However, for a simple 2-D game I'd recommend sticking with Core Animation unless you really hit a brick wall, performance-wise, simply because you will write so much less code.
The items I've mentioned so far have all been in the View portion of the Model-View-Controller design pattern. Your controller code will be application-specific, but you may be able to make most of that platform-independent. If you use a simple model, or even one that relies on SQLite or Core Data for persistence, that should be trivial to make work on Mac and iOS with the same code.
A Mac application and an iOS one (even between the various iOS devices) will have a very different core design. You can't just shoehorn something from one platform into another. Games are probably more portable than anything else, but you will still need to do some custom work to reflect the unique attributes of each computing device.