The News of the World thing is of course only the tip of the iceberg; more and more things are now coming to light, and it seems that other tabloids are implicated.
There's a world of difference between what is in the public interests (MPs's expenses; after all, it's our money they're spending), and what the public are interested in (horrific diseases and accidents, horrible things happening to famous people etc). That the second appears to be more entertaining (in a nasty, salacious kind of way) than the former is not the point; we don't NEED to know whether or not Kate's grandfather was a window cleaner.
And then there's the bit in between; things we don't need to know, but in a way are entitled to know, because the people involved have, as it were, invited us into their lives. There are many "celebrities" who do just that. They court public attention when they want it, and while it doesn't exactly bring out the best in the public when the press revel in the marital break-ups or the perceived cellulite of these people, they have more or less asked for it. And if you're going to call your poor wretched child Harper Seven, people are bound to, well, notice, aren't they? Complaining about press interest in these cases would be like inviting people round to your house, and then slamming the door in their faces. You either want publicity, or you don't. Presumably you have to take the rough with the smooth.
On the other hand, there are people like the Browns (Gordon and Sarah) and the Dowlers, who have been visited by tragedy, and never invited the press in, but they barged their way in anyway. This is absolutely unforgiveable.
Lastly, there are people like (for example) J K Rowling and Judi Dench; people at the top of their game, who could presumably have made millions by inviting Ok or Hello into their homes, but have always opted to remain private individuals. They deserve to have that privacy respected, because they never sought to exploit their celebrity status. They leave that to others. And, let's face it. There are plenty of those.