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The documentation of getattr_static says:
"The only known case that can cause getattr_static to trigger code execution, and cause it to return incorrect results (or even break), is where a class uses __slots__ and provides a __dict__ member using a property or descriptor. If you find other cases please report them so they can be fixed or documented."
I'd like to report another case: when an object's __dict__ is an instance of a dict subclass which overrides dict.get:
>>> _sentinel = object()
>>> 
>>> class MyDict(dict):
... def get(self, key, default=_sentinel):
... print('Hello World!') # This code will execute
... if default is _sentinel:
... return super().get(key)
... else:
... return super().get(key, default)
... 
>>> class X:
... def __init__(self):
... self.__dict__ = MyDict()
... 
>>> x = X()
>>> inspect.getattr_static(x, 'foo', 0)
Hello World!
0
>>> 
(In line 1072. _check_instance calls MyDict.get: instance_dict.get(attr, _sentinel).)

The fix is to use dict methods rather than accessing members through the instance. It will have to wait until 3.2 is out now though.

Apparently another way to get getattr_static to execute code in Python 2.3rc3 is simply the following.
>>> class Foo:
... @property
... def __dict__(self):
... print("Hello, World.")
... return {}
... 
>>> import inspect
>>> inspect.getattr_static(Foo(), 'a')
Hello, World.
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
 File "/home/name/opt/lib/python3.2/inspect.py", line 1130, in getattr_static
 raise AttributeError(attr)
AttributeError: a
>>>

Attached is a patch that fixes the issue: The dict methods are now used directly and before every access to an instance's "__dict__" attribute, it is checked that that attribute is really the instance's attribute and not a class attribute of the instance's type.

__dict__ as a property is documented as an exception to the "no code execution" claim.
The patch is not sufficient - instances may have a class member "__dict__" whilst still having an instance __dict__. Alternatively the "__dict__" property may be provided by a base class and so not available in "type(obj).__dict__" but still be provided by a property.
I don't think there is any general way to tell whether fetching obj.__dict__ will get an instance dictionary or fetch a "__dict__" member from the class or a base-class... (Hence the documented exception.)

> The patch is not sufficient - instances may have a class member "__dict__" whilst still having an instance __dict__.
Sure, but I don't think there is a way how you can access the instance
__dict__ in that case inside Python code. At least I can't think of
one.
>Alternatively the "__dict__" property may be provided by a base class and so not available in "type(obj).__dict__" but still be provided by a property.
>
> I don't think there is any general way to tell whether fetching obj.__dict__ will get an instance dictionary or fetch a "__dict__" member from the class or a base-class... (Hence the documented exception.)
Why not? ``obj.__dict__`` will fetch the instance dictionary iff there
is no class attribute "__dict__" in any of the base classes. In the
patch,``type.__dict__["__dict__"].__get__()`` is used to get (without
any doubt) the class dictionary. By looking inside that dictionary, we
can now tell whether "__dict__" is overwritten: If it isn't
overwritten, the dictionary either doesn't have a "__dict__" entry at
all or the value is a getset_descriptor. So we just need to iterate
over a type's mro, look inside each entries' dictionary and stop when
a "__dict__" entry is found.

Updated patch.

New changeset 8c7eac34f7bf by Michael Foord in branch '3.2':
Closes issue 11133. Fixes two cases where inspect.getattr_static could trigger code execution
http://hg.python.org/cpython/rev/8c7eac34f7bf 

The new entry in Misc/NEWS says: "Patch by Daniel Urban." But it wasn't me, who made the patch, I just opened the issue.

New changeset 382cb3386d57 by Benjamin Peterson in branch '3.2':
correct patch ack (#11133)
http://hg.python.org/cpython/rev/382cb3386d57 

Thanks Daniel (and sorry Andreas). Benjamin Peterson has fixed this.