Microtransactions were once suggested as a solution to this problem, but credit card transaction fees destroy the profitability unless these are collected regularly and then charged in bulk. Some startup could sell NetBux, so a $0.05 microtransaction could be transferred free deducting from a $5 balance; credit card companies would only get a cut for that single $5 purchase. However, unless every browser manufacturer integrates NetBux support, it's dead in the water. Since everyone and their grandma would want to own the NetBux standard and take a cut of that, the most viable option is Bitcoin: it's free, noone owns it, it already exists, and has widely supported infrastructure.
Your browser would have a new UI element that lets you type in a redemption code for a Bitcoin card you buy at a store, or you can import from a wallet. It'd also have as part of the UI what your balance is. If you go to the landing page of say CNN.com it'd advertise prominently what the cost per story is. Click on a story, and before it pops up, the web browser asks if you accept the charge and tells you what the cost is. If you accept, then that amount is deducted, with an option to 'remember for this site.' This site would then be whitelisted, but only at the agreed-upon fee. The whitelist would need to only work for certain subdomains, or something, so that an official page could charge you, but not user content (comments, complementary webpages ala Angelfire, email, etc.) Perhaps it'd involve signed certificates; if you want to charge to access a page, there's no excuse for it not to be encrypted.
It'd be anonymous enough for most people, and porn sites would love it: "click this video, only 3cents; access this photo gallery for 2cents".
It'd also make it trivial to finally implement the 'paid prioritized email' idea, so that non-spam would make it through filters by being accompanied by a 'gift' of a couple cents.
One downside is that it'd be an obvious target for malware; have your botnet send their $5 to your anonymous account. Tying a credit card to the browser to auto-refill the balance would be even worse. There'd also be young kids who click 'accept' on the 'deduct $1.00?' prompts not realizing it's real money, and parents who are sick of refilling their kids' browsers, wondering where that money is going.