It would also be useful to point out that there is a shortcut in the
interpreter itself (PyObject_RichCompareBool, in object.c) which checks
the equivalent of id(a) == id(b) and bypasses __eq__/__ne__ if so. 
Since not every call to __eq__ passes through this function, it's fairly
important that implementations of __eq__ return either True or
NotImplemented when id(a) == id(b).  Ditto for extension modules;
anything that installs its own tp_richcompare should handle object
identity and __ne__ in substantially the same way, so that subclass
authors can rely on the documented behavior when overriding __eq__.