is it possible for my someone to steal your network key and steal game passwords using a program?

If you have WEP security only, yes, it is "technically" possible, especially by experienced hackers.

WPA or WPA2 wireless security, it is very unlikely (not impossible, but takes a long time, and a lot of resources...most hackers would not bother)

If anyone has your WPA2 security key because you gave it to them, then yes, they can capture all the wireless packets, and eventually get all your user ids and passwords....

very unlikely

if you're talking about games you play over the internet then almost all games use some type of encryption so the password/user name is scrambled. and they usually talk directly to the game sever, and dont send information all over your network.

worse that could happen is your neighbor someone copying a keylogger and seeing everything you type. but installing a keylogger like that is.. well also very unlikely.

but if he does have your network key he can/maybe able to view any shared files/folders on your network