Nytimes.com charged for certain types of low-value content--things like columns and op-eds that weren't essential to most readers and that, in some cases, were available free of charge in other newspapers thanks to the NYT's own syndication efforts.
I think a paid subscription model (as opposed to a micropayment or pay-per-view model) might work for a handful--and only a handful--of top-tier national and international publications. I might pay US $5 a month for access to NYTimes.com, for example, but I wouldn't pay for access to the Web sites of the NY Post, The Sun, or the Podunk Yokel-Crier.
For top-tier media sites (NY Times, Times of London), it might be worth charging a small subscription fee not only to get the subscription revenue, but also to deliver a higher-quality audience to advertisers. As things stand now, the demographics of a site like NYTimes.com are almost certainly far less desirable than those of the same newspaper's print edition. And demographics are all that a general news site has to offer, since a relatively small percentage of a news site's coverage is devoted to topics that attract high-paying niche advertisers.