Well, my collection of games isn't as illustrious as some others on here, so I don't know how the stories of games I own compare to others. Nevertheless, I'll give this a shot.
My favourite of all is probably Warcraft 3: Frozen Throne. I've been a devoted fan of Warcraft's story since the "tainted love of Turok and Griselda" days, and consider Frozen Throne to be the absolute peak (I should point out at this stage that I've never played World or Warcraft, or even seen it being played).
Blizzard have always been great at rewarding loyal followers of the franchise, and Frozen Throne is like a treasure trove of loyalty rewards. Kiljaeden, the Dreanei, the Tomb of Sargaras, Draenor itself, Guldan, Rend and Maim... the list of nostalgia pleasing references goes on.
The four campaigns weave great stories by themselves and gel together in one tale brilliantly too (OK, so the Orc one is completely standalone, but let's ignore that bit). The Night Elf campaign pulses with tension, in an urgent pursuit of escaped daemonic prisoner. The Blood Elf campaign sees the final conclusion to the long tale of High Elf misery, started back on Caer Darrow in Warcraft 2. The Undead campaign sees the return of an old favourite, brilliantly held back until the very end of the game to make his entrance all the more dramatic. And the Orc campaign delights in its destruction of the alliances temporarily formed in Reign of Chaos and take us back to old school "Orcs vs Humans" days. Did I mention the return of Lord Admiral Daelin Proudmoore?
Bottom line, I love the storyline of this game, and its wonderful contribution to the series as a whole. Who can honestly say they didn't get goosebumps as Arthas ascended the Icecrown Glacier?
Does Enter the Matrix count? In isolation, the game's story makes little sense, but I love it for its contribution to the brilliant film Matrix Reloaded (which is better than the original film incidentally. Try telling me different). Very Matrixy-ey. It's the only part of the whole series' lore that explains the Oracle's new body!
Killzone gets an honourable mention for being a brilliant idea supported by a great opening cut-scene, only to be spoiled by its pretty poor execution. Real world references make the bits of info you get about the Helghast brilliant ? their appearance, motivation for war, the opening military rally and even their flag. Unfortunately, once you get through the first few missions, the story devolves into 50,000 arguments between Rico and Hakha, meaning it gets tedious quickly.
Finally, I?ve always been a sucker for Tekken?s storyline, and Tekken 4 is right at the top for me. From the resurrection of Kazuya to the darker evolution of Jin, the game creates a wonderful 3-way family conflict within the Mishimas which is great to watch from three different perspectives. OK, so the game isn?t a lengthy complicated story, but what is in there plays out in a very compelling way.
In reference to other people?s choices ? Goldeneye: Rogue Agent? What the hell? The story is bizarre and nonsensical by standards of James Bond fan-fiction, let alone the movies and other games. All there is to the plot are flimsy and unconvincing excuses to bring in as many film villains as possible. And who thought it was a good idea, in a game who?s only selling point is ?It?s good to be bad? to make your enemies OTHER BAD GUYS? So that the plot (defeat an evil supervillain using a doomsday device to take over the world) plays out EXACTLY THE SAME as a normal Bond game?
Everything or Nothing was better, but not great. There?s some great voice acting in there (Pierce Brosnan, Judi Dench, John Cleese, Wilhelm Dafoe) to try and make the story more compelling, but there?s not really a great deal of substance there. Whilst, in contrast, the fact that the game has dozens of action scenes (ie. Levels) means that there is far too MUCH stuff to make a movie of it. Good game though.