Should some parts of celebrities' lives be off-limits to the public, or is giving up privacy a fair price for being famous?
Giving up privacy isn't a fair price for being in the political sphere, and/or publishing, producing, or performing under your real name. Quite frankly, it isn't enough, but I'll settle for it.
You can choose to live a quiet life, but as soon as you step onto the public stage in any form, from a publicly accessible comment on a forum to starring in the latest movie, you become a public figure in my eyes and lose all the protections of being a private individual. Those around you lose the right not to have your life turned upside down by anyone who wants to look. Furthermore, anyone -- celebrity or not -- who pushes his or her personal details and associates onto the public, loses all moral right to deflect any comments made about those details or people. If you mention you have a kid and talk about how you interact with your child, you cannot then use that kid as a shield when someone criticizes your parenting.
That being said, I don't think that the paparazzi should be allowed to literally blockade some celebrities the way they do. There's a difference between taking a picture and impeding your target's path. Sheesh! Get out of the way.