Oh man. Let's see....by myself, it was probably Pokemon: Fire Red or Leaf Green...it's been forever since I actually COMPLETED a game. :/ Sad to say. But if we count doing a co-op campaign, I'd have to say Super Smash Bros Brawl. Which is still pretty old, but I actually remember doing that.
I have a mad tendency to start a game then get distracted by other life things, not play it forever, then get frustrated when I pick it back up again and forget everything that had happened plot-wise. So story modes aren't completed very often anymore. :/ Boo.