Law 1 states that “the field of play is divided into two halves by a halfway line”.
Law 11 states that a player is not offside if “he is in his own half of the field of play”.
I assume that I was correct when I flagged two players this past year for having a foot on the halfway line (but not over), since the player (technically) was not in his/her half of the field. However, some seasoned refs told me that having a foot on the half way line should not result in being called offside when that player received a pass.
USSF answer (April 3, 2008):
Technically, if any part of a player that can legally play the ball is past the midfield line, they are in the opponents’ end of the field and could be in an offside position — depending on the positioning of the opposing players. That counts head, feet and any other part of the player that can legally play the ball — but certainly not the hands. If the referee finds that this player is in an offside position and becomes actively involved in play from that position after a teammate plays the ball in his or her direction, then he or she should be declared offside.