How to avoid having class data shared among instances?

You want this:

class a:
    def __init__(self):
        self.list = []

Declaring the variables inside the class declaration makes them "class" members and not instance members. Declaring them inside the __init__ method makes sure that a new instance of the members is created alongside every new instance of the object, which is the behavior you're looking for.

The accepted answer works but a little more explanation does not hurt.

Class attributes do not become instance attributes when an instance is created. They become instance attributes when a value is assigned to them.

In the original code no value is assigned to list attribute after instantiation; so it remains a class attribute. Defining list inside __init__ works because __init__ is called after instantiation. Alternatively, this code would also produce the desired output:

>>> class a:
    list = []

>>> y = a()
>>> x = a()
>>> x.list = []
>>> y.list = []
>>> x.list.append(1)
>>> y.list.append(2)
>>> x.list.append(3)
>>> y.list.append(4)
>>> print(x.list)
[1, 3]
>>> print(y.list)
[2, 4]

However, the confusing scenario in the question will never happen to immutable objects such as numbers and strings, because their value cannot be changed without assignment. For example a code similar to the original with string attribute type works without any problem:

>>> class a:
    string = ''


>>> x = a()
>>> y = a()
>>> x.string += 'x'
>>> y.string += 'y'
>>> x.string
'x'
>>> y.string
'y'

So to summarize: class attributes become instance attributes if and only if a value is assigned to them after instantiation, being in the __init__ method or not. This is a good thing because this way you can have static attributes if you never assign a value to an attribute after instantiation.