My wife runs with me and she has been experiencing numb feet during and after her run. Does she need new shoes? I believe her shoes are cross-trainers, not running shoes. Has anyone experienced this? What did you do?

Getting good running shoes that fit my feet helped. .

Ditto. Her shoes may be to small.

The first thing would be to look at the laces, I now run my laces up the sides of my shoes and most shoes have two laces for this very reason, it allows my arch to be able to expand, also I wear orthopedic inserts which support my arch and this makes it worse if you don't do it, then your pinching off your blood supply like an arch sandwich with orthopedic insert on the bottom and tight laces on the top plus its worse on some shoes depending if the shoe has more or less support or cushion in the arch area. I also have considered cutting the tongue down the middle in order to free up the arch.

Yup, been there done that. You don't want to tighten the laces like you would with hockey skates, your foot will swell during longer runs. There are some lacing tips at http://newbalance.com/techcenter/#/lacing/ which are kinda interesting, especially the "wide forefoot narrow heel" that uses two pairs of laces. The "top of foot pain" might be worth a try. It's great that you and your wife can run together, get her some well fitted running shoes and keep her on the road.

Thanks for the link! I've been having problems with my left foot (sore ball of foot and numb toes) and am going to try the lacing from here to see if it improves.

This could also be something called compartment syndrome. I have had it and it went away. I have had a friend who had it and she had to have surgery on both legs (this was extreme, of course). If this keeps up she may need to go to a sports medicine doctor.