I think that for
nonmathematicians, a small explanation would be in order.
Ralix states that anything divided by zero is infinity. Excluding
bananas, and other nonnumbers which
ariels has been kind enough to point out, let me be so bold as to exclude many other things, and assume that
Radix is talking about
real numbers (or for the nonmathematicians  any number that YOU would consider to be a number). Two types of people will say that anything divided by zero is infinity:

People who don't know enough and think that it's true (which ariels showed nicely that it's not), and
 People who use it as a short form of "when a number is divided by x, as x approaches zero, the result approaches infinity."
The latter is what people like my first Calculus professor and myself and Cantor mean when they say that y/0 = infinity.
Let's look at 0 / 0 using that definition. A number cannot be divided by zero (that's what asymptotes on graphs are there for). So, zero divided by x, as x approaches infinity, is zero. When x=0, it is undefined.