It's actually a pretty simple answer. Famous people are people that everyone has in common. Think about this for a minute. We gossip about people we know, usually people gossip the most about acquaintences rather than close friends because they remove themselves just enough from the potentiality of negative consequences if they're caught.

Very few people know celebrities personally, yet we all know who they are. I say Leo DiCaprio and you know who he is, he's an actor, he was in Titanic. You get the idea. You also know about who he's dated, Giselle Bundshen, Bar Rafaeli. Because of current and instant media, it's easy and almost impossible to NOT know things about these people. There for, because this infomation is proliferated into the mainstream culture we all have easy access to it.
We all have the subject of the article in common, they're the acquaintence that's very far removed from consequence.

So, why do we want to have all those random strangers talking about us.. Remember, they don't always say such nice things.
That's where things get a little complicated. There's more than one reason. If a person is like me, they suffered from low self esteem growing up. When one has low self esteem, seeking validation from the outside world is a strategy that many employ. As confidence grows, so does a person's extroverted traits, making a person more likely to be in attention grabbing situations.
Because of the instant star status that can be granted to a person, it can be a sudden rush of recognition that can be confused with acceptance. That's where things can get dangerous. If people start behaving in a way that is perceived as being accepted, there is positive reinforcement of the behaviour that created the sense of acceptance.
Like Sue Sylvester from Glee has said, a stadium full of people could be either cheering or booing. It's all in how you take it. Either way, it's just a bunch of people making a lot of noise.