I see that going from Python 3.1.1 to 3.1.2 
instances of io.StringIO no longer have a __dict__ field.

Why?  Is this to make them unpicklable?

I'm not sure why that is. Note that you can still set and get arbitrary attributes, so there must be a dict somewhere, but it isn't exposed. Also, there wasn't any significant change in StringIO in the 3.1 line.
Benjamin, do you have any idea?

>>> s = io.StringIO()
>>> s.x = 5
>>> s.x
5
>>> s.__dict__
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: '_io.StringIO' object has no attribute '__dict__'

Actually it already fails with 3.1 (I tried "hg up v3.1")
Then I played with "hg bisect", and unsurprisingly it answered:

Traceback (most recent call last):
  File "<string>", line 1, in <module>
AttributeError: '_io.StringIO' object has no attribute '__dict__'
Changeset 51991:3049ac17e256: bad
The first bad revision is:
changeset:   51991:3049ac17e256
user:        Benjamin Peterson <benjamin@python.org>
date:        Wed Mar 04 00:14:51 2009 +0000
summary:     merge the io-c branch: C implementation of the io module

New changeset 8ec8a4579788 by Benjamin Peterson in branch '3.2':
add a __dict__ descr for IOBase (closes #12878)
http://hg.python.org/cpython/rev/8ec8a4579788

New changeset fe0497bd7354 by Benjamin Peterson in branch 'default':
merge 3.2 (#12878)
http://hg.python.org/cpython/rev/fe0497bd7354