Can python have class or instance methods that do not have "self" as the first argument?

If you want a method that doesn't need to access self, use staticmethod:

class C(object):
    def my_regular_method(self, foo, bar):
        pass
    @staticmethod
    def my_static_method(foo, bar):
        pass

c = C()
c.my_regular_method(1, 2)
c.my_static_method(1, 2)

If you want access to the class, but not to the instance, use classmethod:

class C(object):
    @classmethod
    def my_class_method(cls, foo, bar):
        pass

c.my_class_method(1, 2)    

static methods don't need self, they operate on the class

see a good explanation of static here: Static class variables in Python