I answered "Only when something of interest to me happens to them", i.e. if a headline catches my eye, or if a celebrity of interest is wrapped up in something that piques my interest, to the extent that I want to see how the saga ends.
Generally, what makes me more interested in particular celebrities is 1) them being crazy/messed up/in a bad situation; or 2) them being really cool, down-to-earth people. Re: #1, I followed Joaquin Phoenix, Amy Winehouse, and Charlie Sheen, during their respective downward spirals, because I wanted to know if they'd get better (or, in Joaquin Phoenix's case, to see if it was a publicity stunt -- which it was, in the end). Re: #2, I think Jennifer Lawrence is awesome and I find her extremely refreshing.
Edit:
To be honest, I would be fine with never reading about them again, but today I am pondering what makes a person even interested in them? I have read/watched them with interest before but I can't quite pinpoint what it is that made me interested. I think it's a little bit more than your run of the mill nosey-ness or boredom.
I've read that it has something to do with a clan/group instinct, where we feel personally invested in those who are prettier/more athletic/more charming/generally "superior", because they're like our leaders? Or at least, our gut tells us that they're our leaders, and we should keep track of them.
Dunno where I read that, though.