I am brand new to Xcode, and I am also brand new Objective-C programmer.
I was wondering if it is possible to create simple Mac games with Xcode. If it's not possible, could you recommend me some good, cheap game engines?
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Xcode can indeed be used to create games. You can do anything a Mac/iOS device is capable of by programming in Xcode.
I think you should focus on what part of the project you want to focus on. As you state you are a brand new Objective-C programmer (welcome). In my opinion it would be quite a mouth full to try and just into Objective-C programming whilst taking on Xcode AND game development (starting with engine design continuing with game design).
If the purpose is to write great games - get a nice engine that fits your needs (3D/2D/??) - have a look at Unity if you like. If the focus is actually learning programming Objective-C and/or Xcode I'd recommend that you make some small utility programs before jumping on to game development. If the point is to simply do game programming consider the alternatives to Objective-C and Xcode - pure C/C++ or even Java.
All that said - I wish you the best of luck in your adventure!
If you'd like to learn Objective-C, I suggest you have a look at cocos2d. It's an open-source 2d engine (written in Objective-C) that allows you to write games for iOS or Mac OS using XCode.
It's not as easy to create games with as with a package like Unity, but there are lots of tutorials (and even books) for cocos2d to be found. A good place to start with lots of tutorials is Ray Wenderlichs site.
Absolutely! XCode is the standard programming IDE for the Mac and iOS. So if your goal is making a game for iOS, you will probably be using XCode along with a few other helping technologies of your choice (e.g. OpenGL ES 2.0).
But since you mentioned game engines I'd also recommend you to use one, since they'll save you a lot of time and effort:
If you are planning to make a 2D game take a look at Cocos2D ( http://www.cocos2d-iphone.org/ ). It's quite popular.
And if you're planning to make a 3D game, maybe Unity ( http://unity3d.com/unity/ ) would be a good bet for you. It's not Objective-C but it can publish for iOS too, if that's your goal.