I think we all can agree that if story can save gameplay, the gameplay (or something else in the game) has to make some sort of effort to be engaging. I mean, otherwise what's stopping you from watching an LP, reading a wiki, or watching cutscenes?
Someone mentioned Psychonauts earlier, and that's one of the best examples I can think of. The platforming is average at best, but it's the storytelling, level design, creativity, Double Fine's blood and sweat etc, that made it so good. I also like the sweeping story of FF7 (I don't care how cliche it is *retreats to corner*) and the gameplay and graphics have aged so terribly.
Though perhaps the best example I can think of is Silent Hill 2. I know a lot of people claim that the shitty gameplay, controls, and camera are supposed to invoke a feeling of helplessness. With me and games like that, it doesn't make me feel helpless. More like angry, maybe even ill with such bad camera work. Not to mention I hate backwards-ass adventure game logic no matter what game it's in. But when I retreat to a Youtube page or wiki, I fawn over the story, symbols, and stuff like that. On the gameplay side, at least the game has some wicked creepy atmosphere.
Drakengard on the other hand, well you have some mildly interesting story told through blocks of text in between about 45 minutes of mashing square to grimey, uninteresting landscapes cutting through stupid cookie-cutter enemies. I keep getting told that the game's story will be worth it in the long run, but then again she loves FF13 lol. I'm sorry, but 6 hours of not having fun isn't worth gawking at the wtf factor of flying demon babies.