I really like the Petrification mechanic from 5th edition D&D. A few creatures have this ability and while there are some slight variations, the gist of it goes something like this (text adapted from various 5e materials):

It takes two turns to fully turn to stone. There is an immediate downside (being restrained) that drastically hampers your combat abilities, but it's not a simple Save Or Die mechanic. It adds a huge, imminent threat to the scenario, but the party will likely have an opportunity to intercede in some way to help the afflicted character. Furthermore, the threat can't be solved simply by depleting hit points.

This mechanic provides a great template for other monster powers with lots of dials to tweak: 

The most obvious and most important adjustment is what befalls the character who fails all their tests. Maybe it turns you to jelly instead of stone. Maybe you become charmed or otherwise mind-controlled. Maybe you combust! This is where the flavour of your power comes from, so it's worth being creative and giving it some thoughts.
The final effect might suggest other intermediate stages than what appears in the petrification mechanic. If you're falling under a mind control effect perhaps you have a harder time attacking your opponents, or take psychic damage for doing so. If you're turning to jelly maybe you struggle to keep a grip on your weapons or are more likely to fall over.

The effect naturally determines which stat you must test. Some kind of poison or venom suggests you must pass a Constitution test. Being enchanted might call for a Charisma or Intelligence test. Being encased in webbing might call for Strength. If you want to go REALLY wild, you might have different stages call for different tests, but that seems kinda bonkers. 

You might also adjust the number of tests that must be passed before the final effect sets in. Adding more stages will generally make the effect easier to overcome as each stage offers a chance to throw off the effect entirely. The petrification effect from 5e uses two stages which I think it perfectly suitable for most cases, especially if the effect is meant to feel fairly dire. A three-stage effect might be less intense, though you can ratchet up the difficulty by imposing disadvantage on all tests after the first or second failure: this creates a small downward spiral that can be difficult to pull out of.

Another dial is the frequency of the test. The petrification mechanic puts the test at the end of the target's turn, which is likely the easiest trigger to remember. This also makes it an immediate combat threat: by the end of next round you might become a permanent installation piece in the beholder's lair!
However, you could make the effect much slower and impose each test after an hour, four hours, or even once per day! This gives the impression of some kind of wasting disease or creeping curse, and may benefit from more stages. It also affords the party more time to find a solution to the problem, reducing the overall challenge.
You could also attach the test to a trigger. Maybe the effect potentially worsens when the character takes damage. Maybe it worsens when the character deals damage. This could heavily impact the choices affected characters make in combat.

There are countless other ways you could change this mechanic: Take a leaf out of 4th edition's disease mechanics and have a successful test not simply cure you outright, but simply step you up one level. Perhaps failing a test causes you to take damage equal to the amount you failed by. I'm sure you can come up with more.

Here are a few monster powers based on turning these dials. I've written them in system agnostic language, so feel free to adapt them to your system of choice:

Wasp Queen's Pheromones
The affected creature must make a Charisma test. On a failure, the creature begins to fall under the influence of the Wasp Queen's pheromones and takes 1d4 psychic damage any time the Wasp Queen takes damage while in line of sight. The affected creature must repeat the test at the end of their next turn, becoming the Wasp Queen's thrall on a failure, or ending the effect on a success.

Jellification
The affected creature must make a Constitution test. On a failure, the creature starts to liquify: taking any physical damage causes it to fall prone, and it must repeat this test every four hours. Failing again causes the target to liquefy further, imposing disadvantage on all tests. Failing a final time causes the creature to fully liquify, transforming into an ochre jelly. Succeeding on any of these tests ends the effect.

Burning Bloodlust
The affected creature must make a Wisdom test. On a failure, the creature is overwhelmed with an insatiable desire to do violence. At the end of each turn, if it has dealt less than 10 damage it must repeat the Wisdom test. On a failure the affected creature's eyes glow like hot coals, it begins belching smoke, and it must attack a creature on its turn if it is able. Failing this test again causes the creature to explode, dealing 1d6 fire damage to all nearby creatures. The effect ends when the creature deals 15 damage in a single turn, or if it falls unconscious.

Fungal Spores

When a shroomling dies, it releases a cloud of spores. All nearby creatures must make a Constitution test. On a failure, affected creatures feel stinging in their eyes and make all tests relying on vision with disadvantage. A creature under this effect which is exposed to additional spores must repeat the test. On a failure they become permanently blind.

Nick Hendriks
Illustrator & Animator