I have lived in Colorado for 32 years, and for me it's always been a shopping cart. Even the signs on the little corrals in the parking lot read "PLEASE RETURN CARTS HERE". But more and more now I hear other shoppers refer to them as "buggies". Even the courtesy clerks at the supermarket I shop at go on "buggy patrol" (when they round up all the carts to return them to the store).
I find it interesting that despite the different terms, retail Web sites invariably use "shopping cart" to refer to the visitor's collection of potential purchases. It seems that "cart" is universally understood, at least in a shopping context, but "buggy" is more limited in scope.
Cart or buggy? Or something else entirely (particularly if you're outside the U. S.)?