Not really a game but a good thought provoking activity that can work well at the end of a devotional or youth service.
Collect a pile of newspapers and bring them along to Youth Group. Get people to come up and tear off a small piece of the newspaper, take off their shoe, place the screwed up piece of paper in their shoe and put their shoe back on.
You'll find when walking around that the piece of paper causes discomfort and will constantly come to the front of your mind. It's a great reminder that when you truely engage with local issues or problems in your local community, it will cause some discomfort or inconvenience. It teaches young people what it means to take up the cross. Most importantly however, give young people an opportunities (either on the night or over future nights) to show what that means in real life; ie sponsor a child, visit a soup kitchen, do a backyard blitz for a family that is going through a hard time, etc.