I don't, but I probably would if I had to (i.e. if the Guardian and the Mail and the BBC and various other random English-language newspapers around the world went paywall, and if the NYT installed a paywall that wasn't so easily subverted!).
But I'd regret it, because if I had to pay a subscription I'd almost certainly only feel able to justify one, so I'd only get one angle on the news.
This is my worry about the digital era generally, if everything goes strictly paywalled and subscription only (i.e. moves to a service model, as music and movies and so many other media are doing) I worry it will make information _less_ accessible than it was in the pre-internet days.
In the days of printed newspapers you would find copies of papers left on trains or in cafes, and could easily read yesterday's news for free. I know that sounds 'cheap', but it's more that it means you encounter a diversity of views, almost by accident, without having to go out of your way to pay for it. Now you either have the paid-for right to read a paper's back-catalog, or it's entirely closed to you. A bit like the way that digital distribution of music and games destroys the second-hand market.
I'm not sure about it, but paywalls and subscriptions seem to me to potentially encourage an information bubble.