Re. football, I've played a lot of mixed 5-a-side football which is a fantastic game - because the court is too small for top speed to matter, and it's all about short, accurate passes, movement off the ball and positional play (and tactical nous) it's a fabulous mixed game.
For 11-a-side (used to play women's Sunday League), absolute speed over, say, 40m, and the distance you can kick the ball (specially in the amateur game which is very much crappy, long-ball-over-the-top) really matter, and that means at an amateur level, relatively few women can hold their own in a mixed game (NB, there is a big nurture/nature question here - I'd think that if more women started to play as children and had the huge number of hours of practise in childhood that most men who keep playing into adulthood have clocked up, things would be a lot more even. One of my closest friends, who played enormous amounts as a child, certainly can - but then, she used to play Sunday league at a level about 4 leagues above me).
Totally agree though that it gives me the rage to see "bikes" and "women's bikes" on websites. Not the fact that one might want to differentiate frame size and proportion by sex (I am 5'3"), but why not have "men's bikes" and "women's bikes"?