I find it acceptable in conversation (sometimes), but not in formal writing. My students (high school) have a very hard time with my "conservative" attitude about it. I don't find it easy to read "their," et al, as singular pronouns.
 
Paul D.
 
"If this were play'd upon a stage now, I could condemn it as an improbable fiction" (_Twelfth Night_ 3.4.127-128).

From: DD Farms <[log in to unmask]>
To: [log in to unmask]
Sent: Wednesday, April 8, 2009 10:33:14 PM
Subject: Any member can give their opinion

At 06:15 PM 4/8/2009, O'Sullivan, Brian P wrote:
> I was wondering whether list members find that it is now acceptable (or at least accepted in some circles) to use "they" or "their" as an alternative to constructions like "he or she" or "his or her"--that is, as a gender-neutral third-person pronoun (as in my subject line).

DD: HORROR! I demur. Keep those agreeable agreements amongst the components of the utterance. 
To join or leave this LISTSERV list, please visit the list's web interface at:
    http://listserv.muohio.edu/archives/ateg.html
and select "Join or leave the list"

Visit ATEG's web site at http://ateg.org/
To join or leave this LISTSERV list, please visit the list's web interface at: http://listserv.muohio.edu/archives/ateg.html and select "Join or leave the list"

Visit ATEG's web site at http://ateg.org/