Just download "Shutter Island" onto your iPod and press the pause and play button randomly. Seriously tho, best story in any movie I've ever seen.
I'd reiterate BASS, Broken Sword and GTA. Driver has a fairly good storyline, told via cutscenes too. Monkey Island has a rather funny storyline too it which is quite good. Rolando 2 also has a decent story too it with a twist at the end, although seeing as we may never see Rolando 3, that might be a bad thing - its a bit of a cliffhanger. And Spider has a rather nice story hidden within its levels. Its not spelled out to you - you have to investigate each level, find the clues etc.
Dear Enviro Bear posters (should say spammers): It isn't that funny anymore. The joke run out of steam, really.