This story may not be so epic, but my FU money gave me some great leverage this week.
Backstory: A few months ago at work I discovered a significant error on a large number of documents, none of which were owned by me or my department. I made the rounds of the "owning" managers, who all looked at the issue and basically said, "Yep, that's a problem". Dissatisfied with this response, I escalated to site management and said SOMEONE NEEDS TO OWN CORRECTING THIS ISSUE. SOMEONE WHO IS NOT ME. It got temporarily assigned to another group, I told them everything I knew about it, and washed my hands of the whole mess.
You know what happened next. I got an email this week from my boss stating that they want me to lead up the correction efforts and a meeting would be set up to discuss it. My boss and I met for another reason a couple days later (before the aforementioned meeting was held), and I said, "Every manager I spoke to about this was unwilling to give any resources to actually fix the issue, and those people are needed. I can't do this on my own, and if I start a project without dedicated resources it's just setting me up to fail. I won't do it."
He clarified that they only need me to do the resource estimates on my own (which I can do), and confirmed that the project won't actually start without those resources being committed. So, I didn't have to dig my heels in like I thought, but my FU money gave me the option if I needed it.
Granted, my boss is a good person, and it's not likely he would have done something that cavalier, but if SHTF, FU money is sooooo awesome.