I think about this all the time.
I didn't make "FU money" from an exit, but rather from the ongoing success of a couple of online businesses, which have been earning me far more than I know how to spend. When this started happening, my initial reaction was to be perplexed, because I no longer had a financial motivation to get up in the morning and work. Money had been the most salient part of my motivation for as long as I could remember.
But I found that I still wanted to work, and it took me a while to understand why. It turns out there are lots of other good reasons to create useful things that people will pay for, like self expression, connecting to others, a sense of achievement, and a feeling of contributing to the world. The money was still nice but became secondary. Still, it allows me the luxury of working on interesting things that I think people will like, even if I doubt I'll ever make much money from them.
I found that the main challenge of being rich is finding a way to spend the money in a way which contributes to my happiness, rather than detracts from it. This is harder than it sounds. The most obvious way to spend money is to buy an oversized home. But this is a really bad idea. First of all you have to spend a lot of time maintaining that home. But most importantly it will likely alienate your (presumably not so rich) real old friends who are still working daily to pay off the mortgage. How will they feel about inviting you over to their condo when you live in a palace?
The solution I found to the "friend alienation" problem is to spend money on personal experiences rather than visible possessions. You can eat out at fancy restaurants, travel the world and enjoy the best shows without your friends knowing what you're up to, at least not in detail. It really helps if you have a spouse and/or children that you can do this with, since they can make these experiences all the more fun.
BTW this also neatly dovetails with recent research on happiness:
http://edition.cnn.com/2009/HEALTH/02/10/happiness.possessio...
The one rich guy possession I'm allowing myself to buy is a second home in a foreign country that I like to visit often. This will (hopefully) make those visits less hassle and more enjoyable, and again, none of my close friends need to know.
And yes, I worry about losing the money a little, and have taken a self-propelled crash course in personal wealth management. But luckily I find the subject quite interesting anyway, and I don't let myself lose any sleep over a couple of percentage points in yield. In the long run, we all die anyway.
To summarize, getting "FU money" been a net benefit in my life, but it took a lot of careful thought and planning to ensure it worked out that way.
Finally if anyone out there who's suddenly landed FU money is feeling a little disorientated by their new situation, I highly recommend reading "Escape from Freedom" by Erich Fromm, which is a wonderful book about the psychological and existential challenges that freedom brings.