NOTE: This post is a direct copy of a reply I made on Facebook a little while back, to a friend who was panicking about the new Facebook messaging app based on this overreactive piece.
Lots of alternatives to FB exist (Google+, MySpace, MSN, etc.), but none are as widely used, and ultimately they all have pretty much the same privacy rights. The price we pay for being able to use all this stuff for free (and it is an immense amount of technology & resource that powers a platform like Facebook) is that to a greater or lesser extent we are the product - they make their money from what they learn about us, and the advertising revenue that information can generate. The article/petition is an overreaction to a minimal change in the situation that has existed for years with Facebook's T&Cs (Snopes' response is much more reasonable!).
I would rest assured that the app will not make calls or take photos without your permission (there would be a much bigger uproar than this if it did!) - but it has to request permission to use the camera/your contact list/etc in order to function usefully. The emotions experiment that James mentioned is no different to what every commercial website in the world does: an experiment with new features that shows one thing to 50% of users and something else to the rest, to see what produces the desired result. This testing (called A/B testing, see here http://en.wikipedia.org/wiki/A/B_testing ) is commonplace but, when Facebook/Twitter/etc. do it, it generates panic.
Ultimately, anything you put on a shared service like Facebook or Twitter or otherwise is to some extent "no longer yours" - but most privacy is an illusion these days anyway. If you use a credit/debit card, store loyalty card, mobile phone, any website at all (even without signing in), you are already being tracked, and this isn't really any different.
Facebook have access to everything you post on the site, but they're not "reading it" in that there's no person staring at your every status or photo - but they are almost certainly running a program that scans all your statuses and reports "hey, we should show this person more nappy adverts because they're always talking about babies," and automatically analyses photos for obvious obscenities, and suchlike.
I would say: carry on using what you're using, be aware of the privacy settings (i.e. make sure you know who you're sharing with), and ask a friendly geek if you have any deeper concerns. Most stories like this are panic-mongering - and often they're doing it because it's the most likely thing to get you to click their link, and earn them some advertising revenue. Cynical, I know, but true.