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os.utime currently requires an explicit `None` as the second argument in order to update to the current time. Other APIs would just have the second argument as optional in this case, operating with one argument.
Attached is a patch which changes the second argument to accept the time tuple, `None`, or literally nothing. Tested on Windows and Mac.
If this is acceptable, I'll make the same change for futimes, lutimes, and futimens.

You have a possible failure here: 
+ # Set to the current time in the old explicit way.
+ os.utime(support.TESTFN, None)
+ st1 = os.stat(support.TESTFN)
+ # Set to the current time in the new way
+ os.utime(support.TESTFN)
+ st2 = os.stat(support.TESTFN)
+ self.assertEqual(st1.st_mtime, st2.st_mtime)
I managed to trigger it after a run of tests:
======================================================================
FAIL: test_utime_noargs (test.test_os.StatAttributeTests)
----------------------------------------------------------------------
Traceback (most recent call last):
 File "/home/antoine/cpython/default/Lib/test/test_os.py", line 286, in test_utime_noargs
 self.assertEqual(st1.st_mtime, st2.st_mtime)
AssertionError: 1320285959.712339 != 1320285959.7133389
Otherwise, +1.

Ah, yes. Would the following work better for the last line?
self.assertAlmostEqual(st1.st_mtime, st2.st_mtime, places=2)

I would specify an even smaller "places". We have very slow buildbots.
You could first call utime() with a date far away in the past if you want.

The `delta` keyword would actually be better than `places`, especially on the slower buildbots. delta=10 would allow up to 10 seconds between those utime calls. Is that being too permissive?

+1 on making the second arg optional.

> The `delta` keyword would actually be better than `places`, especially
> on the slower buildbots. delta=10 would allow up to 10 seconds between
> those utime calls. Is that being too permissive?
I think it's ok. We don't have to test the system's utime
implementation, just that the second parameter does what it should.

+1 to the optional parameter.

New changeset 99e118951a80 by Brian Curtin in branch 'default':
Fix #13327. Remove the need for an explicit None as the second argument to
http://hg.python.org/cpython/rev/99e118951a80 

New changeset 59dca1e2363d by Brian Curtin in branch 'default':
Fix #13327. utimensat now has the atime and mtime arguments set as optional,
http://hg.python.org/cpython/rev/59dca1e2363d 

Changeset 045e8757f10d was also entered for this, which should conclude the changes. Everything seems to have survived the buildbots for now, so closing as fixed. Feel free to reopen if there are any other issues.

New changeset 5e18ff5476e8 by Brian Curtin in branch 'default':
News updates for #13327.
http://hg.python.org/cpython/rev/5e18ff5476e8 

New changeset 8907d646e0df by Jesus Cea in branch 'default':
Commit 59dca1e2363d for issue #13327 introduced a compilation warning
http://hg.python.org/cpython/rev/8907d646e0df