I pay for the news that I read online by having subscribed to them also in paper form, or by paying taxes.
Most other services I use are paid via subscription fees, or are run ad-free by people as hobby projects.
Almost all the ad-supported services I use are monopolies anyway, have strict network lock-in effects, and shouldn't be in private hand anyway, instead they should be run by a cooperative, foundation, or government. (For example, web search, maps, phone books, etc).
This leaves us with a few ad-supported pages which likely couldn’t directly survive in this new environment, but which rely on content creators for their business anyway – such as YouTube.
For such cases, something like Flattr, but paid out by view, would be useful – something like the Datenträgerabgabe for the GEMA and VG Wort, but paid per month, not per empty CD bought.