Or in C# with a string?

If you're going to need to do this frequently, especially if there are more than just a couple of items then you should make a function that does this:

public static bool IsOneOf(string s, params string[] many)
{
  if (many == null)
    throw new ArgumentNullException("many");
  return ((IList<string>)many).Contains(s);
}

You would use it like:

if (!IsOneOf(dog, "cat", "cow"))
{
   Console.WriteLine("A dog is not equal to a cow nor a cat!");
}

This is pretty basic.
A more advanced solution would be to make a generic extension method:

public static class MyExtensionMethods
{
  public static bool IsOneOf<T>(this T s, params T[] many)
  {
    if (many == null)
      throw new ArgumentNullException("many");
    return ((IList<T>)many).Contains(s);
  }
}

You would use it like:

if (!dog.IsOneOf("cat", "cow"))
{
   Console.WriteLine("A dog is not equal to a cow nor a cat!");
}

There are other ways to do this, some optimized for certain cases.