I joined Facebook mostly to get some interaction with distant younger relatives. No one under the age of 50 sends me a snail mail letter anymore.
I too buttoned up as much information as possible.
Some of the youngsters send me requests through Facebook that required I accede to letting the app see my personal information. I said yes. So far so good.
I'm not saying that there are no harmful Facebook apps or games out there, just that they are not all harmful and nothing has bitten me yet that I know of. Before I accept any request from a new app, I go to the page for that app and see what other users have written about it. If it doesn't allow users to write on the page, I don't use it.
The farm game that I play, for example, is standard in that you can send "gifts" to all your friends, or just the farm friends. It has to know who your friends are to send the "gifts".
But you are not the only person I know that has chosen to not play games just because of the reason you cite.