I’ve occasionally paid for sites for a month or so in the past, but I loathe renewing costs. I am a member of a couple sites that simply charge one time or modest, <$30, annual fees.
For larger sites free content with advertising seems to be the model that works best. Smaller ones often get by with merchandising and asking for donations.
Another model that sometimes works is providing decent, free, advertising driven content, with extra premium content that requires a subscription fee.
It depends a lot on the site, but the ones that seem to work are those that are labors of love or recreation by the site creators who manage to attract enough traffic to break even or turn a small profit through advertising.