Back in March we reported on a proposed patch to CyanogenMod that would allow users to deny apps access to certain permissions while retaining the connection to others. This lets users install applications they are interested in, while remaining mindful of their privacy.
Update: Indeed, the "faking data" patches did not make it into CM and probably never will - thanks to all who posted the correction, including the patch author. See this commit for more info.
Denying permissions unfortunately has a nasty side effect - they will cause applications that don't handle the situation correctly to force close. If an application does start force closing and you've revoked some permissions, you will see a special dialog to easily reset those permissions back to "stock" and give the app a second chance.