I agree with palewriter that ‘him or herself is "correct," but what about the real English that has found its way forward in our daily speech: Themselves!
In the sense of: "Everyone should pick up their ticket(s) at the door."
-Or-
"I hope that anyone who is feeling ill today will kindly excuse themselves from wrestling!"
I call this the "false plural of ambiguity."
Current and tres moderne!
Sitran