Look through them without emotion.
Me:
I'll probably look them in the eye and chirpily say hello when we cross paths.
On a semi-related note, I owned a sweet pair of shoes some 10 odd years ago that really clacked while you walked. You'd be suprised at the amount of people who'd cross the street if I was walking up behind them just to get rid of the ominous sound of someone following them. Oh, the sense of power one gets from intimidating a stranger just by walking behind them. 
Yup, that's me. People kind of stopped crossing the street once I started leaving my sword at home while going for a walk. Still convinced it was the shoes though.
I have studied a book by Edward Hall called, The Hidden Space, which deals with non-verbal communication through a spatial lens.
He observed how non-verbal interactions vary depending on the relative density of like-species in a space.
So if you were to cross paths with someone while walking on a trail where you only see someone every 10 to 20 minutes, your reaction would be different if you were in a city where hundreds of people cross your path each minute.
Likewise, for me, my reaction changes on the density of population and setting. In a hospital (as I've had many experiences with lately), I've mastered the concerned but approving nod. In a city street, I tend to actively ignore everyone. In the situation described, due to its awkwardness, I'd probably offer a high five.
I don't know if I raised it here or with Foolz privately, but I got on an elevator the other day, and I was going to the third floor with three others in the elevator. The first person got off on the second floor. I turned to the stranger next to me and said, "Look at that loser; he couldn't handle it, not like us, we're going all the way!"
Someone is walking towards you from the opposite direction. Do you look away? Stare? Assert alpha male dominance?