I'm surprised no one has mentioned the following. (I have heard it explained this way several times; I feel there are some disadvantages to it, but I'll let others articulate them if they so desire.)
In mathematics, definitions that are difficult to apply to concrete models often are developed to be consistent with already established patterns. (Aside: In higher arithmetic, for example, we expand nonnegative integer exponents into negative integer exponents and then to rational exponents.) We agree that positive times negative is negative (yes?). Then, for example,
3*-3=-9 2*-3=-6 1*-3=-3 0*-3=0
In each case when we add subtract one to the first factor, the product is increased by 3. Now, to keep the pattern consistent, -1*-3 must be....
(Of course, the introduction would have to be reworded for elementary students....) Comments? Is this just as bad as "that's the rule"?