In the original rules, vampires, wights, wraiths and specters who drain a victim of all life cause the victim to return as a lesser-strength undead of the same type. Or, at least, they are able to do this to "man-types". This probably just means human or near-human, but people have occasionally questioned whether this should apply to elves, dwarves, or halflings.
Screw what it probably means; let's assume that only human beings can return as vampires, wights, wraiths and specters. Everything else drained of life-force is just dead, usually, but maybe rises as a zombie, and every once in a while, as ... something else. Roll 2d6 when a non-human is drained; if either die is a 6, the corpse rises as a zombie; on double 6s, a race-specific undead variety returns. So what would these varieties be?
Here, I'll do dwarves as an example. I'm assuming that corporeal life drainers (wights, vampires) might make a slain dwarf return as something corporeal... let's call them "tunnel-corpses". Their unholy drive is to destroy underground structures and wall up tunnels behind explorers to trap and kill them. The non-corporeal undead bring slain dwarves back as something non-corporeal... call them "chasm spirits". They become one with stone floors and cause cracks to open up; on a successful "attack", a chasm spirit catches an explorer's foot in a crack and slams the crack shut again, trapping the explorer. They then cause a cave-in to try to kill the victim.
So, what would be good variants for other races?