If I have a class like below:
class Point(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y
And have 2 objects:
a = Point(1,2)
b = Point(1,2)
How can I modify class Point to make id(a) == id(b)?
class Point(object):
    __cache = {}
    def __new__(cls, x, y):
        if (x, y) in Point.__cache:
            return Point.__cache[(x, y)]
        else:
            o = object.__new__(cls)
            o.x = x
            o.y = y
            Point.__cache[(x, y)] = o
            return o
>>> Point(1, 2)
<__main__.Point object at 0xb6f5d24c>
>>> id(Point(1, 2)) == id(Point(1,2))
True
When you need a really simple class like Point, always consider collections.namedtuple
from collections import namedtuple
def Point(x, y, _Point=namedtuple('Point', 'x y'), _cache={}):
    return _cache.setdefault((x, y), _Point(x, y))
>>> Point(1, 2)
Point(x=1, y=2)
>>> id(Point(1, 2)) == id(Point(1, 2))
True
I used a function alongside namedtuple because it is simpler IMO but you can easily represent it as a class if needed:
class Point(namedtuple('Point', 'x y')):
    __cache = {}
    def __new__(cls, x, y):
        return Point.__cache.setdefault((x, y), 
                                         super(cls, Point).__new__(cls, x, y))
As @PetrViktorin noted in his answer you should consider the use of a weakref.WeakValueDictionary so deleted instances of the class (doesn't work with namedtuple apparently) don't remain in memory since they remain referenced in the dictionary itself.
You need to have a global dictionary of objects, and get them through a factory function (or a custom __new__, see the other answers). Additionally, consider using a WeakValueDictionary so that you don't unnecessarily fill up memory with objects that are no longer needed.
from weakref import WeakValueDictionary
class _Point(object):
    def __init__(self, x, y):
        self.x = x
        self.y = y
# Cache of Point objects the program currently uses
_points = WeakValueDictionary()
def Point(x, y):
    """Create a Point object"""
    # Note that this is a function (a "factory function")
    # You can also override Point.__new__ instead
    try:
        return _points[x, y]
    except KeyError:
        _points[x, y] = point = _Point(x, y)
        return point
if __name__ == '__main__':
    # A basic demo
    print Point(1, 2)
    print id(Point(1, 2))
    print Point(2, 3) == Point(2, 3)
    pt_2_3 = Point(2, 3)
    # The Point(1, 2) we created earlier is not needed any more.
    # In current CPython, it will have been been garbage collected by now
    # (but note that Python makes no guarantees about when objects are deleted)
    # If we create a new Point(1, 2), it should get a different id
    print id(Point(1, 2))
Note that a namedtuple won't work with WeakValueDictionary.
If you need to compare whether your two objects house the same values, you can implement the eq operator:
>>> class Point(object):
...     def __init__(self, x, y):
...         self.x = x
...         self.y = y
...     def __eq__(self, other):
...         return self.x == other.x and self.y == other.y
...
>>> a = Point(1,2)
>>> b = Point(1,2)
>>> a == b
True
>>> b = Point(2,2)
>>> a == b
False
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