When Descartes says, "I think therefore I am", what sort of argument is he using? Is he simply saying, "There is an X, and X thinks, therefore there is an X", in which case he might as well have said "I walk therefore I am" or, with Barbara Kruger, "I shop therefore I am"? Or is the argument here more esoteric?

I can't do better than to refer you to Section 4.1 of this SEP entry: http://plato.stanford.edu/entries/descartes-epistemology. It even addresses the specific question "Why I think rather than I walk?"

Read another response by Stephen Maitzen
Read another response about Philosophers