Each application comes with a list of permissions that it needs (or wants) to work - access the internet, read personal data, monitor phone calls or SMS, etc. You're notified about those when you're about to install an app from the Android Market, and need to agree to them. So you should
ask yourself (for example): does a game really need access to your address book data?
(Internet access is pretty common, actually - it's needed to display ads, for example. I don't generally worry about it unless the app also wants access to sensitive data.)