I have to echo Eliezer's fear of useful spending. I have some contingencies, but I could not absorb that much money intelligently.
To spend any fraction of that, you'd need an organization, and synchronizing an organization's goals with my own is another hard problem.
If it's existing wealth, then destroying the unusable portion of it does make everyone else proportionally richer, at least until the markets recover. If it's new wealth, then probably the best thing to do would be to stabilize existing selected markets with enormous and slow moving investments, until I could determine what to do.
Out-of-context quote of the day:
From Simon Johnson, Director of the IMF's Research Department, on "The Rise of Sovereign Wealth Funds".
So if you had $10 trillion, what would you do with it?