I'd like to believe that I would somehow discover a hidden treasure trove of ambition, hindsight, wonder, curiosity and lust. But, realistically, I don't think I'd do very much at all. Take, for example, right now. I have finished my exams, done as well as I had hoped for, and now am facing the burden of extended freedom. There is so much of something, in my particular case, this is time, that I have no idea what to do with it. I flounder and dream, all the while the time I'd been waiting all year for passes, indifferent to my ambivalence.
Perhaps I would go around the world, or donate to all the charities I can and become the next modern saint, perhaps I'll start my own country, or buy an island, or move to the Neptune- who knows? Maybe I'll become mad with power and wealth, and end up alienating those around me, and become a hermit living on the side of a mountain in the Himalayas. I would presume that a life in which one does not have to struggle to make ends meet is a very comfortable existence indeed, and is free from very much suffering at all. Nietzsche, when we were studying him this year, said that suffering was the mother of human ingenuity, that it unlocks "man the creator" and helps build him. I tend to agree with him on this, due to both personal experience and what is entailed if suffering ceases, namely hedonism. Somewhat naïvely, I think that people tend towards hedonism and selfishness in such cases, due to the overabundance of choice, which causes them to fulfil their wildest fantasies without a regard for their financial wellbeing. Now if this is a beneficial usage or waste of time is completely subjective.
The decisions surrounding what to do with the money would come fast and compulsively, I suspect. After all- you do have all of the money you will ever need. But after a point, I think it is pertinent to say that there is only so much you can do within a certain time period. If one does spend their lives jet-setting around the world, buying big and indulging, there is a fair chance, in my opinion, that one won't die any more fulfilled than one who did not receive this blessing. Ultimately, that is the end-game, right? To be happy in your life and die knowing you've lived it to the fullest? A lot of philosophers think so (Aristotle, Parfirt and Callicles (in a regard), The Stoics).
I just think that the money aspect of the life would quickly overrule the other parts that make life such an experience, such as struggling, suffering and having those ambitions and dreams that drive a person, that I fear maybe lost or quenched once someone has all the money they'd ever need, resulting in stagnation and/or long-term indecision.
I don't know- just some thoughts from some cooked carbohydrates

Link for those interested in a more scientific view of happiness:
http://www.theatlantic.com/magazine/archive/2009/06/what-makes-us-happy/307439/