Unspecified number of parameters in C functions - void foo()

That's an old-style function declaration.

This declaration:

void foo();

declares that foo is a function returning void that takes an unspecified but fixed number and type(s) of arguments. It doesn't mean that calls with arbitrary arguments are valid; it means that the compiler can't diagnose incorrect calls with the wrong number or type of arguments.

Somewhere, perhaps in another translation unit (source file), there has to be a definition of the function, perhaps:

void foo(x, y)
long x;
double *y;
{
    /* ... */
}

This means that any call to foo that doesn't pass two arguments of type long and double* is invalid, and has undefined behavior.

Prior to the 1989 ANSI C standard, these were the only kind of function declaration and definition available in the language, and the burden of writing correct function calls was entirely on the programmer. ANSI C added prototypes, function declarations that specify the types of a function's parameters, which allow compile-time checking of function calls. (This feature was borrowed from early C++.) The modern equivalent of the above would be:

void foo(long x, double *y);

/* ... */

void foo(long x, double *y) {
    /* ... */
}

Old-style (non-prototype) declarations and definitions are still legal, but they're officially obsolescent, which means that, in principle, they could be removed from a future version of the language -- though since they're still around in the 2011 standard I don't know that that will ever actually happen.

There is no good reason to use old-style function declarations and definitions in modern C code. (I've seen arguments for using them in some corner cases, but I find them unconvincing.)

C also supports variadic functions like printf, which do take an arbitrary number of arguments, but that's a distinct feature. A variadic function must be declared with a prototype, which includes a trailing , .... (Calling a variadic function with no visible prototype isn't illegal, but it has undefined behavior.) The function itself uses macros defined in <stdarg.h> to process its parameters. As with old-style function declarations, there is no compile-time checking for arguments corresponding to the , ... (though some compilers may check some calls; for example gcc warns if the arguments in a printf call are inconsistent with the format string).

This literally means that you are not telling the compiler what arguments the function takes, this means that it will not protect you from calling it with any arbitrary set of arguments. You would need to say in the definition precisely what arguments are actually taken for the function to be implemented however.

You could for example use this if you were generating a header file to describe a foreign function in external code, however you did not know what the function's signature actually was, it would still then be callable using your header but if you provide the wrong arguments in the call results are undefined.