Mass effect series (i refuse to elaborate, play the dam games)
Gears of war series (there is crap going on even if the characters refuse to acknowledge it, or if it is incredibly poorly explained)
Half Life series (even if you just look at half life 2 and the episodes there is a lot going on there)
Halo series (i refuse to count each as it's own game, there is a massive story here, but unless you're willing to devote enough time to earn a PHd in Halo-ology then your probably not gonna see it)
portal (see mass effect)
borderlands (there was a story... but the game seems to forget about it in favor of killing space alligator dog things)
Battlefield Bad Company (infinitely stronger than any CoD game in that there is character development, but its very linear and ultimately simpler than it wants to be, people find gold and nearly start a world war, some story to be had)