Shadow of the Colossus didn't have any storyline. It was more like really good long sex: there wasn't much to say but it felt really really good.
The thing with SotC and ICO is that they have storylines but they are being told very differently than your normall game. That's one part of why they are so good.
You can't have the topic about best storylines and not mention Silent Hill 2. IMO it's THE best storyline ever.
Planescape: Torment
Final Fantasy Tactics
Final Fantasy VII
Max Payne - it's not very complicated or original but it's complete. No plot holes (or almost none and small ones), great main character, great storytelling.
God of War - same as Max Payne combined with very fulfilling ending.
Mafia - good storyline combined with great atmosphere.
I also like Odin Sphere a lot.
Sanitarium has nice storyline.
Games I am yet to play/finish and I think they have potential to end up on the list above:
Tactics Ogre
Eternal Darkness: Sanity's Requiem
Final Fantasy V/IV
Xenogears
That's it for now.