Which programing languages can be used for publishing to the Mac App Store? What are the programing language requirements for publishing to the mac app store? Obviously Obj-C is the main one, but can someone publish using something like C++? Or Java?
The rules for the Mac App store are converging towards that of the iOS App store.  The iOS App store currently allows the use of almost any programming language (even Basic or Assembly), as long as everything required for that language (code, interpreter, runtime, libraries, etc.) is bundled with the app.  For instance, many iPhone games have a built-in Lua interpreter or a C# runtime.

If a language used by an app requires any separately installed support other than that built into the Lion Mac OS distribution, the review guidelines say that app will be rejected.  Cocoa and webkit (for Javascript) are currently built into the Mac OS X distribution.

So, if you want to use Java, you might be able to get away with including your own complete JVM and all needed runtime support libraries for Java in the app bundle.

BTW, XCode supports using C++ and Objective C++ code, as well as Objective C and its plain C subset.  But you may have to use some Objective C APIs to make an application compliant with all the UI guidelines, even in a mostly C++ app.