I'm not sure that you're referring to the Amazon or Paypal type sponsorship. Those are not free to click. Those are were you want to invite your visitors to reach into their own pockets to contribute to the running of your service, which you will continue to offer.

If I understand you correctly, you are looking for schemes whereby you invite your visitors to click on a link, in return for which some third-party sponsor will make a small donation to the cause. There are many examples of this, here's just one famous one: www.thehungersite.com - see the big yellow button in the center. I just clicked on that and 1.1 cups of food was donated.

What is it you want to do? Do you want to collect donations for the worthy cause of your choice? Are you looking for donations for your own service? Are you looking to increase clicks to an existing donations site?

If you're looking to collect donations for an existing cause, contact them. They may already have sponsors who would be willing to participate.

If you're looking to find sponsors for your own service, then you will have to find the sponsors.

If you're looking to increase clicks to an donations site, just link to them.

For the first two, once the sponsors are in place, the next step is counting the clicks so as to calculate what the sponsors owe you. Writing a simple click counter is very easy, but the sponsors probably won't want that. They will expect some measure of protection against
- you just making up numbers
- any one of your visitors clicking a million times a day
- any of your visitors writing a script to do that
- you paying people to click
- people getting spammed to click
- etc etc

This is where the programming gets tricky, and may require ongoing finetuning to ensure that both your cause and the sponsors get a fair deal.