`he' vs `they'

What pronoun to use, when the gender is unspecified?

1. "The winning photographer will have his portfolio published."
2. "The winning photographer will have their portfolio published."
1. "The next attorney general will have to defend his viewpoints."
2. "The next attorney general will have to defend their viewpoints."
1. "I'm going to stop the next synchronized swimmer I see, and kiss him on the cheek!"
2. "I'm going to stop the next synchronized swimmer I see, and kiss them on the cheek!"
1. "After finishing your turn, your opponent will have his chance to respond."
2. "After finishing your turn, your opponent will have their chance to respond."
Clark Gable and Claudette Colbert starred in the mentioned movie:
1. "Each of the Stars of It Happened One Night won an oscar for his performance."
2. "Each of the Stars of It Happened One Night won an oscar for their performance."
[This example taken from the American Heritage College Dictionary, in a usage discussion under "he".]
1. The reader's eye shouldn't balk; good prose will be transparent to him."
2. The reader's eye shouldn't balk; good prose will be transparent to them."

The first thing to note is that the problem can usually be resolved with a simple re-phrasing:

But sometimes this isn't possible; what alternatives are there?

Some approaches, and their drawbacks:

Just defaulting to "he" is clearly wrong. Worse -- in a society where sexism is still a problem it's outright detrimental. And if you're writing (say) a game, and your instructions all presume only male players, at some level you're alienating some females from your game, needlessly reducing your audience a little bit.
"They" is my personal favorite. It is becoming increasingly accepted and used, and it sounds natural. Admittedly, it's gramatically incorrect, but it's more correct (and less harmful) than implying a specific gender

Though there are still a couple of situations where it's particularly awkward:
- If the antecendent could be an unspecified individual or a group: "If somebody defies the council, they will be sorry!" As with all ambiguous antecedents, nice editing can fix (and often improve) the sentence: "The council will regret the day somebody first defies them."
- As a possessive pronoun, a generic-singular "their" is awkward:
  1. "The next attorney general will have to defend his prdecessor's policies."
  2. "The next attorney general will have to defend their prdecessor's policies."
  (Hmm, as I re-read this later, the second option sounds just fine...)

Other, less satisfactory?, approaches include:

Defaulting to "she" isn't quite as bad; although it's wrong, it doesn't perpetuate historical exclusions/disencouragements.
Alternating uses of male and female examples isn't too bad, though personally i find that distracting when reading: I keep thinking there is a reason why one gender or the other has been chosen for that example.
"He or she" or "he/she" is admittedly a bit unwieldy. However, after playing Magic: The Gathering a while, all their cards using the construction "his or her" seem entirely natural to me.
"s/he", prounounced "she", is a nice idea. [Heard from Donna Haraway.] Perhaps "hisr" or "heriz" would be the other forms?
A science fiction book (by David Brin??) used "er" for the indeterminate form of "his/her"; it took me quite a few pages to figure it out, and i never really grew accustomed to it within one book, but it's a nice idea.