First I wanted/started to write something about distributing Bandwidth via proof-of-work units (aka. difficulty 1 Bitcoin mining shares) and financing traffic with these, but I think this can be even more generalized:
A lot of people would like to do some micropayments (for buying farmville carrots or whatever), but Bitcoin is not exactly tailored for transactions this small. Also users would need a fully fledged Bitcoin installation + some way to get Bitcoins in the first place, which they might not want to do for whatever reason(s).
The worth of a single 1 difficulty share is [current average worth of 1 bitcoin block] / [current difficulty] which currently would mean a share equals 50.01/877226.66666667 = ~0.000057 BTC.
If difficulty goes up more, this value will go down further, as the reward per block goes down (I don't expect transaction fees to go up THAT much that a single block on average still will be worth more than 50 BTC like currently EVER), the value per share goes up again.
Just enter your hostname, their account name (if there is one required, could be just tracked via IP as well, if it's a "live" setting for getting limited time access to content for example)
Imagine getting 1 Rapidshare credit for every 100 shares you submit instead of BTC or even a completely new one-click hoster that is 100% financed by mining - the more shares you submit, the more bandwidth you get. No ads or other restrictions needed!
Additionally, since you as operator use BTC anyways, you can even sell these "credits" for BTC below "market value" (example: 10 000 credits for 1 BTC which would give you credits "worth" 0.57 BTC) to make users not solely rely on mining (Laptop users...)
Using existing tools like the Bitcoin mining proxy, such a system could be done already today and to reduce variance, you could relay shares from many/all pools and just submit the (verified) results from your users as your own, like the mining proxy does. If the share is then also accepted by the pool, credit the user with 1 unit of whatever you use to track their contribution and there you have it.
* Can be extended with Bitcoin payments and "mining credits" can be sold to users for BTC as well
* No Bitcoin needed AT ALL if your Users don't want it - you can even code your own miner and rebrand it to whatever you want
* Users are keen to generate revenue for you, no way of cheating (proof of work!)
* Users get advantages too for working for you, benefitial for both parties
* no hassle with mining for you, but still income from mining instead of buying at exchanges with volatile rates
* More users, more costs, more income
* Ads and other stuff STILL possible
* Users at least are required to run a web applet, if not even a full Bitcoin miner
* Mistrust what "these calculations" really are, as nearly everywhere where I've seen people advertising mining
* If you remain hidden about what you're really doing (see compute4cash who let you mine and pay out ~50% of the USD generated), this can hurt your reputation
* If you rely on income from BTC, potential tax regulation issues (talk to a professional!)?
* Laptop users/users with weak GPUs (nVidia is kinda okay if you don't charge HUGE prices, many still generate 1 or more shares per minute) are either not in your target group or a bit excluded/forced to pay - expect some hate from them