Is it necessary to include __init__ as the first function every time in a class in Python?

No, it isn’t necessary.

For example.

class A(object):
    def f():
        print 'foo'

And you can of course use it, in this manner:

a = A()
a.f()

In fact you can even define a class in this manner.

class A:
    pass

However, defining __init__ is a common practice because instances of a class usually store some sort of state information or data and the methods of the class offer a way to manipulate or do something with that state information or data. __init__ allows us to initialize this state information or data while creating an instance of the class.

Here is a complete example.

class BankAccount(object):
    def __init__(self, deposit):
        self.amount = deposit

    def withdraw(self, amount):
        self.amount -= amount

    def deposit(self, amount):
        self.amount += amount

    def balance(self):
        return self.amount

# Let me create an instance of 'BankAccount' class with the initial
# balance as $2000.
myAccount = BankAccount(2000)

# Let me check if the balance is right.
print myAccount.balance()

# Let me deposit my salary
myAccount.deposit(10000)

# Let me withdraw some money to buy dinner.
myAccount.withdraw(15)

# What's the balance left?
print myAccount.balance()

An instance of the class is always passed as the first argument to a method of the class. For example if there is class A and you have an instance a = A(), whenever you call a.foo(x, y), Python calls foo(a, x, y) of class A automatically. (Note the first argument.) By convention, we name this first argument as self.