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.

You declared "list" as a "class level property" and not "instance level property". In order to have properties scoped at the instance level, you need to initialize them through referencing with the "self" parameter in the __init__ method (or elsewhere depending on the situation).

You don't strictly have to initialize the instance properties in the __init__ method but it makes for easier understanding.

So nearly every response here seems to miss a particular point. Class variables never become instance variables as demonstrated by the code below. By utilizing a metaclass to intercept variable assignment at the class level, we can see that when a.myattr is reassigned, the field assignment magic method on the class is not called. This is because the assignment creates a new instance variable. This behavior has absolutely nothing to do with the class variable as demonstrated by the second class which has no class variables and yet still allows field assignment.

class mymeta(type):
    def __init__(cls, name, bases, d):
        pass

    def __setattr__(cls, attr, value):
        print("setting " + attr)
        super(mymeta, cls).__setattr__(attr, value)

class myclass(object):
    __metaclass__ = mymeta
    myattr = []

a = myclass()
a.myattr = []           #NOTHING IS PRINTED
myclass.myattr = [5]    #change is printed here
b = myclass()
print(b.myattr)         #pass through lookup on the base class

class expando(object):
    pass

a = expando()
a.random = 5            #no class variable required
print(a.random)         #but it still works

IN SHORT Class variables have NOTHING to do with instance variables.

More clearly They just happen to be in the scope for lookups on instances. Class variables are in fact instance variables on the class object itself. You can also have metaclass variables if you want as well because metaclasses themselves are objects too. Everything is an object whether it is used to create other objects or not, so do not get bound up in the semantics of other languages usage of the word class. In python, a class is really just an object that is used to determine how to create other objects and what their behaviors will be. Metaclasses are classes that create classes, just to further illustrate this point.