Is main() (or Main()) in C, C++, Java or C#, a user-defined function or a built-in function?
I'm not sure what you mean by built-in vs. user defined. Almost no language actually gives your user-defined function the privilege of being the true entry-point into the program. C++, any .NET language, and Java all have hidden (built-in) entry point methods that in turn call your user-defined Main method (or whatever the entrypoint method for that language is called -- in .NET it can be named anything, although C# and VB.NET force it to be called Main).
So yes, virtually every language has a concept of a method that is automatically called, and this method is a user-defined method and usually mandatory. But virtually every language also has a built-in entry point method that actually sets up the framework and/or memory management for the process before invoking your user-defined "entry-point" function.
It is not "built-in" in any language, in a sense that there is no standard implemented-for you main() avialable.
For C/C++/Java, it is a function with a special property, namely, the function that will be called at the start of your program after all the static setup is done. E.g. entire C program's execution path is:
Do some initialization code
Call main()
Exit.
As such, it has a standard declaration (# of parameters passed from command line + array of "strings" - however the language implements that - which are the actual arguments from command line)
In Java main(String[] args) is the entry point for applications by convention (to make C++ programmers comfortable). For applets or servlets the invocation of code happens differently. Note that a jar may contain any or none of these entry points and that each class may contain a main so a given jar can be invoked in many different ways as an applcation if so desired.
It's declaration is built-in. It's definition is user supplied, or in some cases supplied by an application framework that has some other entry point, or in the case of most event-driven GUI frameworks, no single user-defined entry point.
It's a user defined function that is called by the language's runtime library. For example, a C runtime library will grab the command line arguments and sometimes environment variables from the operating system and pass them into to your main() function.
Different language runtimes usually perform the same operation in one form or another, and will throw some sort of error if the function it tries to call doesn't exist.
It's a required user defined function (the entry point for executables)...