I want to mention chrono trigger (Snes, PS1 or DS) especially which had me hooked from beginning to end.

Monkey Island has not yet been mentioned.

The Thief series had some interesting storylines...

Tom Clancy has his name plastered all over a number of series...

etc.

Planescape Torment has the single greatest story in gaming history, riveting, epic in scope yet so intimate that each character’s struggle become your personal burden, you cry tears of joy at their triumph and lament with them at their failure. Just about every single character, even the obligatory side quests fillers are fully developed, making you feel like you experiencing a living breathing world. Word fails me at just how amazing this game really is but I’ll give it my best shot.

What can change the nature of a man? A story that spans millennia started with this single question, or rather; a question that was asked long before the game ever started like a long ago legend that is intimately connected to the protagonist. History and memory intermingle as you play a amnesiac immortal who wakes up in a mortuary in the company of a floating talking skull and with only a tattoo edged on your blue-skinned back giving you the first clue to start a story that will takes you from the land of dream and belief to the very bowl of hell itself.

On the way you meet an interesting cast of characters that range from the intense to the bizarre, each as vivid and full of history as the protagonist, each as lovingly crafted as the main character of an epic novel. Together you and your companion delve into your forgotten past, experiencing trial and tribulation, finding knowledge, wisdom, painful memory and love in all its form. Slowly you piece back your memory fragment by tormenting fragment until all that is left is the question that has haunted you for a near eternity; what can change the nature of a man?

A game that last the test of time, because its story is timeless; no other game has ever come close to making its story sing to you like a siren, its haunting melody lulling you into oblivion with a sad melancholic smile of absolute contentment.

That teahcer of yours definitely isn't no video game fan if he doesn't think there's any good storylines in games.

Metal Gear Solid 3! (Or even the MGS series): There was so many twist and turns in that game I didn't think my heart could keep up, there was such a sad ending I nearly started bawling. IMO MGS3 storyline beats pretty well any movie I watched.

Also the Final Fantasy VII series. Especially FFVII and FFVII: Crisis Core. Again with FFVII there was so many twist and turns that I nearly took a heart attack. And also with Crisis Core it had one of the saddest endings to any video game I've ever played.

Other games with good storylines:

God of War

Zelda: A Link to the Past

Most Final Fantasy games

Assassin's Creed

Resistance (After playing 2 I have to get 3!)

Uncharted had an interesting storyline

Shadow of the Colossus has a very different storyline to most games.

Good stories in videogames died with the point-and-click adventures.

Oh wait, there's Phoenix Wright. Nice stories, decent character development, sort of amusing and plenty silly humor.

Majora's Mask

mibuokami,

+10 for u !!!

Been comming to this site a fair while and haven't felt the need to post until now as no-one seems to have mentioned Deus Ex!

Deus Ex is probably the greatest story heavy game I have played and remains my favorite game of all time. The story is rich and twisting and you have multiple outcomes dependent on your actions.

I think others that need a mention are:

Final Fantasy VII
MGS series
Half-Life series
God of War series
Mass Effect
Star Wars: KoToR
Bioshock

Seriosuly though, if you haven't played Deus Ex, go buy it!

Final Fantasy IV
Suikoden II
Final Fantasy IV

MGS Series
Suikoden II
Tales of Symphonia (I guess)
And probably Xenogears

The Metal Gear Solid series has the storyline thing on lock.

Crisis Core: Final Fantasy VII
Final Fantasy VII