I was thinking about this too. That "pay us 300 dollars in bitcoins to get a key to your data" virus could be like that.

If the payment -> key sent part was automated then money would just build up in the bitcoin account over time.

You could also automate the backend – set it up so that the botnet could draw on the BTC account to purchase new VPS hosting for its command and control servers, migrate when the old ones get taken down, etc.

Of course, without the creativity to come up with new C&C mechanisms, the pattern of migration and purchases might eventually become predictable enough to stop the botnet.

More concrete example:

Make something that scrapes content and SEO-izes it. Add affiliate links. Run on AWS. Make payout to affiliate commissions to the same account that pays AWS. Make the system capable of growing/shrinking its AWS capacity on its own. bam. self-perpetuating and potentially self-optimizing/growing income with zero outside intervention (except for when google corrects around it).

I think this is an interesting example but it doesn't address the concerns that a single actor could modify the program behavior at will, making the system hard to trust if multiple parties are trying to benefit from it. I believe a key idea of autonomous corporations is the inability of a single participant to alter it's function without consensus of other participants.

Does anyone have an example other than the BTC blockchain that provides a valuable service guaranteeing consensus is required for changes to the system's behavior?

Seems like consensus is the tricky part. In the case of the affiliate link example, where all of the business is online, you could host the code under a version control system that allows people to fork and modify the code, but requires majority approval for that code to get deployed. Also if all of the financial assets are in BTC, you could have a corporate wallet that is governed similarly (so expenses and disbursements need to be approved by the majority). Of course this isn't exactly an 'autonomous' system, more like a decentralized system.