The media does unfairly hound famous people in order to improve ratings or sell more copies of the publication. While it is acceptable to write a story about anything and freedom of the press is important, chasing someone down in the street for a photo or invading someone's private property is not fair and in most cases is either illegal or bordering on illegal.
"Famous person" is a vague distinction, as it could pertain to a prominent musician, actor, politician, activist, or simply a member of a prominent family. While it could be argued that some "famous people" ask for the scrutiny and treatment they receive in the media (for example, Kanye West and his outbursts, or Paris Hilton and her partying), there are many others who are judged for even the smallest of things. The British royal family comes to mind immediately - they are constantly in the eye of the media and paparazzi, and anything from what outfit the royal baby is wearing to what Kate Middleton looks like in a bathing suit is front-page tabloid material. Consider also actors and musicians who are passionate about their art, but wish to have a modicum of privacy when they're not performing. They stand little chance of being able to walk down the block without a camera in their face, waiting to catch them in a moment of frustration, which then would be touted in the news as an outburst of rage or a sign of some family turmoil. This is not how anyone should be treated, and the media is largely to blame for the practice being perpetuated.