Unfortunately, people are often not quite rational about small amounts of money. If one earns $12.00/hour, then $0.001 represents 0.3 seconds of earnings. I'm certain that many people would think for several seconds each time they click such a link. Some people would be very concerned about accidentally spending too much.
One solution to such concerns might be to form larger membership groups. For example, a user might pay $1.00/month for a basic membership, and 10 cents might go to the group administration. The remaining 90 cents would be split among the sites the user chooses from a subscription list. At the end of each month the group would send a single payment to each of the member sites with its share of the total amount.
Problem: it costs more than the value of the payment to process a payment.
Solution: pay a large amount sometimes rather than a small amount all the time.
So, for instance, when I go to a website demanding a .001 payment, I don't pay every time. Instead, I pay .50 to every 500th site that I visit demanding such a payment. On average the sites make about the same amount of money as they would under the micropayment, but you save on processing fees by aggregating payments.
The obvious dilemma is: how can web sites force users to pay anything at all under this model? You check up on them stochastically. In order to view websites which require micropayments, viewers must buy a membership with a micropayment authority for a small fee ($5 or so). They also give the authority to charge a credit card in the future if they refuse to pay. They are given a permanent cookie that contains a member identifier.
Each month or so, participating sites submit (parts of) their server logs to the authority. They also submit logs of the money they were given by the users. The authority audits the logs and gets a rough estimate of the amount of hits that viewers have made to various sites. From this the authority can estimate what the viewer "should have" paid. The authority then compares that to the total amount of money that each user has contributed. If any user is found to have underpayed by a substantial amount, their credit card is charged what they owe plus a punitive fine ($10?).
There is a maximum amount that any site may charge any user per time period ($10?)
Of course, auditing every user and every log may be a substantial amount of work. Some users and some logs could be randomly chosen instead.
Users can partially "beat the system"; if they know that only 5% of the server logs are audited, they can compute the chance of getting caught times the punitive fine and weight that against the money they save by underpaying by certain percentages (because if you don't sample all logs, most of the places that a user visited probably won't show up each month; so a user can divide their payments accordingly). They can then reduce the amount that they pay by the computed amount. However, this is not really a big problem; say it is optimal to pay 100 times less than what you should. Vendors simply charge a penny where they would previously have charged a hundreth of a cent. At that price range, you still aren't scaring off many viewers. And most people will be honest anyhow.
Users could commit blatent fraud by letting a million people use their account and then cancelling their credit card and disappearing. This will happen a lot; however, most people will be honest and will not use such systems.
At the end of the day, even with widespread fraud site operators will still make much more money than they would now. Right now, most webpages that would be priced in the micropayment range either don't exist, are provided free, or have a non-micropayment monthly fee which scares away 99% of the users who would user the service if it were cheap.
There is an excellent article by Clay Shirky called Fame vs Fortune: Micropayments and Free Content  showing that micropayments are doomed to fail because creators are not publishers -- these days creators have the tools to publish online, and they crave attention more than money. Therefore, there will always be free content available, if the publishing cost is (close to) zero. At the same time, micro payments have a constant mental transaction cost -- is this article really worth 10 cents? Is the abstract worth 1 cent?
If a reader submits a correction by postcard to the editors of a traditional encyclopedia, it will take a significantly larger effort by the editors to check the facts and introduce the correction into the next edition, than it took to send the postcard. This kind of transactions have therefore not been practical. Wiki is a technology that does away with the transaction cost and enables the transfer of minimal contributions of work effort.
If a similar technology had enabled the transfer of minimal contributions of money, then we would have the much sought after micro payments.
This doesn't mean that it is easy to appreciate the value of a wiki work contribution. That appraisal would still require something corresponding to the editors checking the facts. An inserted "not" in the right place can either save an article from error or ruin a correct article. That wiki can be useful despite this deficiency is explained by the fact that the reduction of the transaction cost also makes it possible for other readers to correct errors and that it thereby becomes meaningful for the readers to spend energy on checking facts.
Perhaps this wiki thought pattern can be useful in figuring out how to implement micro payments.
See MicroCredit for more "small scale finance" possibilities.