Yes, there is an offside penalty in American Football. The neutral zone is defined as the area extending from the tip of the football to each side of the field, so the neutral zone is as wide as the length of the football. No player, except the center, may have any part of his body in the neutral zone at the time the ball is snapped, otherwise they are guilty of being offside. On a kickoff, no player may have any part of his body across the line upon which the ball rests prior to the kick, except for the holder if one is used. The penalty for offside is 5 yards.
In the NFL, the penalty is 15 yards. In college, the penalty is 10 yards.
In college football, the penalty is 15 yards. In the NFL, the penalty is 10 yards.