The Fire Emblem series have great storylines. I really liked it. Story is very important to me, and I like having cutscenes and such to explain it. Good cutscene graphics /=/ in-game graphics for me. Story FTW!

Not necessarily complex but a good storyline must have some deeper meaning to raise it above the average action flicks dominating hollywood right now. A good storyline must also have developed characters, must be original and non predictable and have an overall storyarch that is engaging.

 If you took away the gameplay from Zelda TP or Uncharted and simply released them as movies they would fail, miserably. And that says quite a lot considering that you're average holywood storyline is quite shallow as it is. Purely as story's TP and Uncharted are quite bad.

Well gameplay comes first, obviously, if not then it can't be a good game, we all know that. But a good story sure does help. :)

 A game's story does not need to be original to be good.  It just has to be interesting and engaging with twists and turns to keep you guessing until the end.  TP and Uncharted's stories are actually pretty good.  Many critics praised Uncharted's story if I remember correctly

The Secret of Monkey Island games had my favourite story lines. Weird but damn funny if only more games would be like this.

 I fail to see how Uncharted's storyline is even as good as your average Holywood action movies, which are quite shallow in themselves. Like I said, if you released those games purely as movies they would fail miserably much less ever hope to win any awards for their storylines,

It mainly depends on the genre. A FPS would need a very good gameplay and nice action and a decent storyline, but an RPG should focus more on an amazing storyline but it should also aim for good gameplay, interaction and other features.

 I disagree. For me storyline comes first, even if the gameplay is bland or average a good storyline can save the package. Of course gameplay is very important, but for me storyline is even more so.