story is an important part of game.a bad story can turn a game bad.

It depends on the genre. A story or method of storytelling that works well for an RPG probably won't work too well for a racing game.

My friends all rave about Metal Gear Solid, though I myself never got into the series.

For my money, I'll take games like Puppeteer, Kid Icarus: Uprising, and Half-Life 2 that develop the story during gameplay segments rather than frequently bringing the players' interaction to a complete halt for the purpose of showing them what happens. I also like the Dark Souls method of keeping most of the story in the background, allowing players to disregard it entirely or to delve deeply into the lore if they so choose.

Alan Wake and Deus Ex.

Story: Xenoblade Chronicles
Storytelling: Metroid Prime

Can I just say the Metal Gear franchise

That I can think of off the top of my head, I'll say Portal 2.

Mass Effect Trilogy

Deus 'The-Best-Game-Ever' Ex

Xenoblade has the best story.

Suikoden II.