I have to say, as much as I love the combat parts of Dark Souls, I love it for its storytelling just about as much.
It's so rare to see a game which doesn't try to spell everything out for the player either through constant chatter between characters or (worse still) extensive cutscenes. Dark Souls constantly tosses bits and pieces of background on the setting and the characters at players via visual clues, small snippets of dialogue, and lore found on item descriptions; a lot of care was put into building a world and even more care was put into ensuring that players could discover it at their own pace and in their own ways - pieces of equipment which would simply be junk in just about any other game often are worth seeking simply because of the information they reveal.
On top of this, it's so very, very nice to see a game tell a story which isn't necessarily a happy one. Just about any character arc (let alone the main plot) has a bittersweet ending at best and a terribly tragic one at worst; Dark Souls doesn't try to be 'edgy', it's simply a depressing world which only gets worse the more you learn about it. The limitation to one save slot per character is an especially nice touch as every decision made gains a weighty air of finality and any accidents are irreversible.
In short, Dark Souls is a testament to the power of passive storytelling and I really wish we could see more of it since video games have proven to be a wonderfully powerful medium for this type of storytelling if only developers would learn to utilize it instead of bludgeoning players over the head with exposition-laden cutscenes.