I want to accept credit cards on my site without having to go to a third party provider and without monthly fees.
We all want this. It will never happen, and actually, look for fees to increase given the current financial crisis as with less credit transactions, gateways and providers will look to offset the decrease in income.
There would be no point for any company to do that. They are in the business for a profit so there is no way you would ever find a company to do it for free. I hate the fees but Paypal is not bad for the little guy. If you get into bigger number, you can save more on the fees with other services. However, you will never reach the free point. If you find one, go the other way because they will not last long and when they vanish so will your money.