Wraiths

Wraiths have a strong visual identity: hooded, faceless black figures. They are the Grim Reaper, the Ghost of Christmas Yet to Come, the Nazgul, even the Dementors (if you must). They look scary. Everyone knows the empty cowl means death. 

My own drawing

D&D doesn't know what to do with them. Are they corporeal? Do they paralyze or Energy Drain? Are they Nazgul or is that Spectres? It all depends on which edition you prefer. Delta has a great round-up. 

With their intimidating visages, wraiths should advance the thesis that I've explicated in previous posts (skeletons, zombies, ghouls, wights) that each undead type ought to be uniquely terrifying. 

My wraiths are of the semi-corporeal, black mist mode of wraithdom. They'll look solid enough, but your glaive-guisarme passes clean through. Unlike wights, wraiths don't have names or personalities. They are anti-life voids, avatars of nihilistic hatred. They just want to snuff all the candles. 

The Lord of the Rings: The Fellowship of the Ring (2001)

Death Spirals Revisited

These guys are brutal. They've got auto-hit life drain (don't worry, I won't make you deduct levels), dissolution at 0hp (no save, no res) and escalating damage that snowballs like a motherfucker.

This monster sets up tactical puzzle-fights and is a bit more mechanically complex than my previous undead. They can float over obstacles and flow between people, so fight positioning will be unusual.

Instead of the canonical level-drain, I've given the wraith an area-of-effect aura. Wraiths deal damage to all adjacent creatures, with no roll and the monster gains the hit points taken. This damage increases every round. The party needs to win fast or it will get out of hand. 

The goal here is for the players to fear them. For their arrival to be an "Oh, shit!" moment, without having to resort to level drain.

Muppets

Wights

As the appellation Wight once referred to men, so too the creatures thus called were once mortal lords. Now they are bitter undead, who loathe and envy the living. Their visages are bleached and their personalities eroded by time, until nothing remains but fierce hostility and simmering resentment. 

They were lords and still believe they should be. 

My own post-it drawing, referencing this one by Vance Kelly

A Boss Suitable for Low-Level Parties

The wights in my game are an undead boss monster. I want something that can stand on its own thematically, not just a stronger zombie with "No. Appearing 2-16" and level-drain. 

A wight should have a name and a story.

In my version, I hope to bring back the dread and vindictiveness of the Tolkien original and evoke the draugr sagas they were based on (e.g. Grettir, Hrómundar and Hervör's saga, perhaps the barrow-dragon from Beowulf). Fun fact: the original use of the term "barrow-wight" was by William Morris in his Grettir's saga translation. I also thought of M.R. James' "A Warning to the Curious" and its BBC adaptation. 

Wights haunt the vicinity of their own tombs and must return to them during the day, unless they are deep underground. 

They'll gain the ability Shuttered Room suggested in their comments section, "undead being vulnerable to weapons that were made while they were still alive, so that rusty old broadsword is of use while that specially imported custom rapier is not." You can reduce them to zero hit points, but they'll dissolve and reform until they're finally dispatched with a suitably ancient implement.

They can track treasure stolen from them, with dire consequences for anyone paid with it. 

You'll think you've defeated one only to have it show up at your campfire a night or two later.

Cairn in Snow (1807) by Caspar David Friedrich 

Skeletons

Van Gogh

Of all the monsters in D&D, skeletons are the one most often depicted in art (of the non-game related sort). They are a constant theme. Drawn, painted and sculpted throughout history. A reminder of the inevitability of our own deaths and the monster that lives inside each of us, hidden behind a mask of meat and skin. 

William Blake

So of course I want to make them into a goofy cartoon monster. I want puppets and stop motion aesthetics. 

When you fight skeletons in my game, I want you to almost see the marionette strings. When you strike a mighty blow, they should burst apart with a clatter of scattering bones.

Disney

If you're going to take an easy, low-level undead fight for granted... these are the ones.

And yet... we still need them to be at least a little challenging to fight. They can't just be a very small stack of hit points.

Harryhausen

Strengths

Unlike the classic skeleton (BX/OSE and 5e), my skeletons are immune to slings and arrows (an outrageous fortune) and take half damage from piercing weapon. This makes them difficult to fight at range or if they are behind bars or a grate. This sets up lots of opportunities for adventurers to be harassed by weak monster that are difficult to get at. The challenge of the fight isn't rolling bigger numbers, it's figuring out how to get from here to there.

A complimentary feature is skeletons' ability to see in the dark and shoot further than torchlight extends. Arrows out of the darkness terrify players. This can be used to good effect to emphasize the importance of light.

Finally, skeletons have time on their side. They don't get hungry. They don't need a pee break or a nap. You can put them in a cage and hang them from the ceiling or brick them up behind an arrow slit. They can be a trap or an environmental hazard.

Weaknesses

In addition to being flimsy, skeletons are incredibly stupid. They are easily tricked. 

Zombies

Maybe it's a fools errand, but I want to make the zombies in my game a little more interesting and threatening. I want my players to be genuinely scared of the undead.

I tried an iteration of this last year that fell bit flat so I've tweaked the recipe a bit.

Justin Moll

Sponge Monster

Zombies should shrug off weak hits and soak up a lot of damage before collapsing. On the flip side, in keeping with the tropes, one really big hit should take a zombie out. 

Instead of giving them a ton of HP, they'll get damage resistance (reduce the damage of each incoming hit by 4).  This will make them very resistant to arrows and small hand weapons. You'll want to hit these things with two-handed swords and polearms.

Deadly Infection

A zombie will first attempt to grab victims. Once grabbed, zombies will make bite attacks with advantage.

Any character bit by a zombie will contract grave rot, a deadly wasting disease that most low-level parties will not be able to cure. Getting bit by a zombie usually means death. 

Grave Rot: Every hour, lose 1/4 of your max HP. Hit points lost in this way can't be healed until the disease is cured. If you die while under the effect of Grave Rot, you'll return as a zombie (or occasionally some other undead). Grave Rot spreads from the point of infection. If it's on a limb, quick amputation can be a viable cure.

In B/X, 2HD crab spiders have save-or-die poison, so this doesn't feel too punitive.

Weaknesses

Zombies are slow and stupid. They always lose initiative and move at half normal human speed. If you can get out of their sight for one combat round, they'll forget you exist.

If a victim is brought down, zombies may stop fighting to consume it, ignoring anyone nearby unless directly attacked.

They are nearly always unarmored and make no attempt to avoid being hit. 

Mummy Hands

Little scuttling horrors. Disembodied hands skittering and leaping -- grasping, driving fingers into flesh with ab-human strength. 

They look like Thing but fill a niche with the face-hugger, the headcrab and the rot grub. An ambush, nuisance monster. Individually weak but very deadly if they slip past your defenses. 

Addams Family (1964)