EFF points to an interesting article The Perpetual, Invisible Window Into Your Gmail Inbox which talks about pitfalls of allowing apps access to one's Gmail, Twitter, Facebook, etc., accounts. It's a good read, though my basic advice is don't give access to your e-mail to any app. However, with a smart phone the temptation might be great.
One of the sites mentioned there is http://mypermissions.org/. I recently deleted my Google+ account and barely use my Windows Live account, so the only account of interest there was LinkedIn. It turns out they think I had given access to two applications, an event announcement app and a survey app. They are probably both innocuous, but I was never aware of giving them access, and actually like the idea of getting rid of their useless event announcements, so I was able to disable them. Also, looking through my LinkedIn settings, I saw a number of settings that they had chosen for me by fiat, as I never would have chosen to allow e-mail from partners, for example. All that is cleaned up, but apparently bears revisiting from time-to-time.
In my Gmail account I had sharing among various Google services enabled and the ability to use my Google account to log in to some services enabled. Basically, if my Google account is penetrated, other dominoes fall.