In the United States, today is 1/11/11. In much of the rest of the world, it's 11/1/11.
That difference is enough to argue against using numbers alone. Although all those 1s look terrific together, numbers alone can't communicate with the clarity of words, especially if you have clients, employees, or business partners around the world.
So, to be clear:
Today is January 11, 2011, or 11 January 2011.
Do you agree?