All my armies have some degree of fluff surrounding them. My two favorites are as follows:
Bork'an Rapid Response Cadre
Faction: Tau Empire
Commander: Shas'o Koshra Vaers
The Story: O'Koshra is a Tau that dreams (which I've decided is an anomaly for the Tau, given their poor warp signature). His commanders think he may be insane, so they have him visit a Gue'vesa'la who happens to be a psychologist (of which there are few in the Tau Empire). His battles are often reflections of his dreams and, sometimes, him reliving trauma from his past. The Ethereals are keeping a close eye on him, in case he snaps.
The truth is that he is being manipulated by the Eldar. They have a grand destiny for him, he just doesn't know it yet.
The Bloody Host of Hrothmog the Rapacious
Faction: Chaos Daemons
Commander: Hrothmog the Rapacious, Bloodthirster of Khorne
The Story: Hrothmog has conquered a subsector of Imperial Space through a warp rift and slain virtually all its inhabitants. Now, bereft of worthy foes, he grows bored, bellowing his challenges deep into the Warp, waiting for someone worthy to challenge him. Most of the time he spends brooding in his great hall, listening to the empty oaths and pointless bravado of his thanes, and occasionally prods the cage of bone in which he keeps the Herald of Tzeentch, Ka'thmagoras, who whispers lies in his ears, seeking to somehow secure his freedom.
I've got others, too. These are the most interesting, I think.