In old school D&D and its ilk skeletons do not get enough love. They're still great to use for every reason skeletons are rad but you don't get much life out of them, appropriately enough. What you certainly don't get out of them is fear.
Yes I can get some mileage out of my players early in the game, especially without a cleric present, emphasizing the macabre, alien intelligence and otherworldly power that a skeleton merely existing autonomously indicates, and the sheer horror of it having a will behind it to boot, the rage of the bones, and all that. But after a couple of skeletons the effect wears off, especially as they level, and especially if they have a cleric because shockingly quickly skeletons just start instantly exploding and where is the fun in that?
You can get a little bit of that "Oh shit" back with skeletons just like you do with goblins, in upper levels, by adding way more of them. But then the thing in question is rarely seen as anything but the abstract, a mass of Other which must be overcome. It's what the human brain does. An army of skeletons isn't an army of individual skeletons, and therefore 10,000 times as scary as one skeleton, it's one army, 1x as scary as the word "army," which is pretty scary but there's no scale to it. It becomes a swarm of bees, still deadly but when you can cast Turn Bees and you've got like three scrolls of fireball you stop caring unless it's close, like at the Super Bowl.
This problem isn't specific to skeletons. I already mentioned goblins, and the normal humanoids have a bit of this as well, but even dragons can suffer from this. "Seen it, let's blow up the cave entrance and starve it out for a while, ho hum."
So does Cthulhu really. Even Cthulhu AS a joke has BECOME a joke, that's how overexposed ol' octopus-puss is. But when you sit down to play Call of Cthulhu even though your team might be cyborgs or army rangers or pulp heroes or (HEY HERE'S A THOUGHT CTHULHU GAMERS) just dudes into weird shit, they're still dwarfed by the awesome spectacle of the horrible, and if they're not then you make them at least a little more terrified for their own characters' lives. That's what we're talking about really: when something becomes known it eventually becomes safe. This is also something the human brain does. But since Call of Cthulhu is a game about fake people with fake brains it can control those brains to endanger them and BY DOING SO constantly change the stakes and situation, meaning that each new skeleton encounter is a BRAND NEW skeleton encounter (because if you can't scare them with monsters, scare them with losing all their crap). It does this with Sanity Checks.
(Quick skeleton-specific aside: I play in a 4e game and my DM loves skeletons because he is a right and just person. 4e solves the problem of "ho hum another skeleton" by having about 800 different skeletons of increasing HP and all kinds of new abilities, even if some of the distinctions boil down to "skeleton with +5 sword" which I could have done that just fine without the whole new stat block guys. What gets less used in the 4e games I've played is what they call an undead template, which you can go through your MM with and use to turn every creature into a skeleton. Not doing this would be boring so of course this is one of the approaches I take with making skeletons in particular more rad. Here's a monster, but it's also a skeleton, describe how weird that is, oh and your cleric needs at least as many HD as the original monster to turn the monster skeleton as a normal level 1 cleric turns a normal skeleton. This would have come up in my current game more if the party stopped trying to kill themselves in new and exciting ways and just let me kill them like I had planned, but as indicated above that's KNOWN and therefore BORING and I might as well get something out of this evening, too.)
This is how I intend to use the back end of Ability Scores to do the same thing:
A character coming face to face with some big holy shit horror for the first time must make an Intelligence check to keep their composure in the face of terrible awful no-good very bad things. This makes sense because magic-users have high intelligence and dealing with horrible things is their job. Passing means he can proceed normally but failing means he gets 1 point of Shock. Points of Shock are cumulative and are only lost under very rare circumstances, like human memories, and can be recovered, like human memories, so even if you get a high level cleric to soothe you you can always have a Nam flashback and be right in the shit again. You have to make a second check when subject to a Fear effect.
A character taking a point of Shock records on the back of their sheet the specific trigger for that point of Shock. Extra xp for players who remember to play these key moments out later, because this is how real fear works. You eventually get to the point where your arachnophobia isn't so bad you can't even be around fake Halloween cobwebs, but they still skeeve you out and you worry a little bit every time you try to flush one that he'll get out of the toiler paper and take your whole hand off.
Characters who incur a number of Shock points equal to their Wisdom score take a permanent 1 point penalty to AC, to-hit, damage, and even HD rolls. This makes sense because clerics have high wisdom because they're more accustomed to fighting evil and horrible things as a job description and so can last longer before cracking from the pressure. When they finally do crack under the pressure, though, it's like a shell-shocked soldier, they're just going to be all-around less useful in the field from then on.
When a character's Shock exceeds their Wisdom score, when their "inner harmony" can no longer keep things together, they begin to go a bit peculiar. For each additional Shock point, they crack and go completely Froot Loops. Gain a permanent behavior disorder, or a disorder their already have gets one major magnitude worse. After 2 game sessions or 2d4 in game days, whichever is longer, Remove Curse can undo one of these effects, but doesn't reduce a character's Shock value. When a character's Shock value reaches 20, they're officially pantscrappingly crazy enough that they're not your PC any more. They're my NPC and we're going to have fun together.
This also means that when generating NPC parties of adventurers or key high level NPCs they all also have a Shock value rolled using 3d6 unmodified, with any appropriate penalties and new effects applied.
Now there are enough awesome insanity tables out there that I don't really need to provide one here...but I will. Roll equal to or under your current Shock value on this chart, re-rolling if necessary. If you end up with disorders that seem to contradict one another you suffer the potential of an Asimov's Law Breakdown, which is also my favorite electric banjo song. Save or be literally stuck arguing with yourself until someone snaps you out of it, giving you a Charisma save to stop acting like a lunatic for five minutes. Except where indicated all other madness saves are also Charisma based, using Charisma since you still may be crazy after the save but you need at least the ability to ACT sane for a short time.
1. Choose an animal. Character screams uncontrollably at that animal in its presence. Roll this result again and they react to any artwork or depiction of that animal. Roll this result again and even the name of that animal or words who sound like it get the same response.
2. Must compulsively steal something useless from every building they enter. Roll again and they do not even try to conceal their theft. Roll again and this applies to all outdoor and social situations as well.
3. Character dissociates and adopts a new identity. Roll again and character also things it's the opposite gender. Roll again and character also thinks it's another race entirely.
4. You agree with everything your friends tell you. Roll again and you agree with everything anybody other than your enemies and monsters tell you. Roll again and agree with anything anybody tells you.
5. You compulsively lie, except where self-interest and self-preservation are concerned. Roll again and you lie even if you lose out by lying and endanger yourself. Roll again and you lie on pain of death, to everyone, incapable of telling the truth.
6. You believe you're in a dream, but you still take effort to survive your dream. Roll again, you believe you're invincible in your dream. Roll again, you believe that you are PART of the dream and one known NPC of the GM's choice is the dreamer you must protect at all cost in order to survive.
7. You believe one innocuous item, animal, or person is in fact deadly. Roll again, you believe one dangerous item, animal, or person is in fact harmless. Roll again, make a dangerous selection and a safe selection; you can no longer distinguish between the two.
8. Lose a language you know, except your alignment language. Roll again, lose an additional language you know PLUS your alignment language. Roll again, you know no languages and have animal intelligence.
9.You only fight with an invisible weapon only you can see and feel. Roll again, you only fight with invisible, invulnerable armor only you can see and feel. Make sure you change the description of these each time. Roll again, not only do you not use other weapons or armor, you go out of the way to destroy other weapons and armor you could use.
10. You sing what you're doing. Roll again, you even sing everything you're thinking with no filter. Roll again, you can only sing, and sing in your sleep.
11. You light small fires whenever possible. Roll again, this extends to your party's stuff. Roll again, this extends to your other party members and to you.
12. General cowardice, and an additional -1 to hit. Roll again, save vs spells when confronted with anything scarier than mundane provincial life or run away as from Fear. Roll again, you get one additional Shock point and make another roll.
13. You become convinced you're actually a zombie. Roll again, you think you're a ghost. Roll again, you think you're a lich, aboog aboog aboog.
14. You kill small things in needlessly cruel ways like Renfield, and must do so whenever possible. Roll again, you feel compelled to hurt your friends, attacking them whenever possible but only doing 1 damage. Roll again, you're compelled to harm yourself, and will inflict 1 damage per attack against yourself as often as possible.
15. You begin worshiping a god nobody has heard of. Roll again, you declare yourself high priest and believe you have cleric abilities or the abilities of a cleric 5 levels higher. Roll again, you are this god made flesh, his only begotten son.
16. You have seething, boiling urges that constantly color your judgments. To begin with, you want to bang everything, party excluded. Roll again, you want to kill everything, party excluded. Roll again, you want to marry everything, party NOT excluded.
17. You see everyone who has ever died, anywhere, all around you, at all times, or think you do. Roll this again and you also hear them, always. Roll it again and you cannot distinguish the visions and voices of the dead from the living.
18. You're possessed by a demon with his own personality and agenda, and must save vs Spells to act in your best interests instead of the demon's. Also, roll again and add that result, too.
19. Roll three times and take each result.
20. Your madness has given you icy clarity to see through the veil of worlds and observe the cosmic underpinnings which lie beneath. Save vs Death or your heart stops or your brain trickles out your ears or something. If you successfully save, roll 1d6. 1-3: you become imbued with one level 9 magic-user spell which you can cast once per day. 4-5: you become a unicorn, retaining the better of your AC/HD/HP or the unicorn's default stats. 6: you're a god now, but not the good kind like you want, and suffer 1d10 mutations.
Now I'm not going to use this system universally but I will use it evenly. Nobody has to save when they see a horse, but everybody has to save when mummys show up, always, even if you sit down at the table with your 2hp and announce you're a world famous mummy slayer (So your PC is an enormous liar, interesting...). This is also a good way for me to put some mechanical meat on the metaphorical bones of how I handle ghosts, but that's other posts. And there'll be weird exceptions. In my Arcis Enumre game, for example, humans and dwarfs from outside this great city have to save the first time they meet a gnome, for example, because gnomes are fucking weird.
And you can bet twice and a half your own ass I'll be using this for some skeletons, monstrous or otherwise.