Does C# support a variable number of arguments, and how?

Yes. The classic example wourld be the params object[] args:

//Allows to pass in any number and types of parameters
public static void Program(params object[] args)

A typical usecase would be passing parameters in a command line environment to a program, where you pass them in as strings. The program has then to validate and assign them correctly.

Restrictions:

• Only one params keyword is permitted per method
• It has to be the last parameter.

EDIT: After I read your edits, I made mine. The part below also covers methods to achieve variable numbers of arguments, but I think you really were looking for the params way.

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Also one of the more classic ones, is called method overloading. You’ve probably used them already a lot:

//both methods have the same name and depending on wether you pass in a parameter
//or not, the first or the second is used.
public static void SayHello() {
    Console.WriteLine("Hello");
}
public static void SayHello(string message) {
    Console.WriteLine(message);
}

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Last but not least the most exiting one: Optional Arguments

//this time we specify a default value for the parameter message
//you now can call both, the method with parameter and the method without.
public static void SayHello(string message = "Hello") {
    Console.WriteLine(message);
}

http://msdn.microsoft.com/en-us/library/dd264739.aspx