I am a huge fan of great stories...The best I've come across lately are:
Knights of the Old Republic : part one or two are both good but part one is the more complete game...Plus the story is better, if you can run it on you're Pc it's a must. Or get the backwards compatible xbox platinum version {it has to be the platinum version because the bugs are worked out and runs in 480}. You must get this game...don't read anything about it, go off of blind faith and play it, if you read something on it you might get a spoiler. We all know spoilers are bad for games with great stories.
Shadow of Colossus: This game is greatness, if you have a PS2 you must own it.
The
Prince of Persia games have a great story involving time travel {who doesn't like time travel}...The Narration is superb {so far only part one is BC}.
And of course
Mass Effect has a great story....It's safe to say Bioware games {
Baulders Gate 2,
Jade Empire} have great stories along with character development.
Oh and lastly
Half-Life 2 has great character development and atmosphere...
Portal is very entertaining because of the story; I get a sense of joy when I play through the game that I have never got playing anything else.
And just because I promote it...
Panzer Dragon Orta has a really good story and is backwards compatible.
I realize I sound kind of arrogant in my post, but these games are that great I want the world to play them...These games are the reason why I play video games. As far as I'm concerned these are must play throughs{que cool pose}
P.S. I would also recommend playing Shenmue 2...But as soon as the game becomes great it ends...I await the conclusion.