Uh, the last game I bought... was, erm, uh.
Well it was a quite a while ago, to be sure. I think it may have been BioShock when it first came out. Hrm, I bought Metal Gear Solid 4 soon after that came out too, but it was for a friend and he reimbursed me, so I'm not sure it counts.
At any rate I'm considering buying a new copy of Jet Set Radio Future. Because I hear MS has, in recent memory, updated the 360's backwards compatibility such that I could play it again. But I was not nice to my first copy (which came with my original Xbox when I bought it), and it doesn't run anyway.