1. The number of houses on fire in a metropolitan area. It's generally around zero. Whenever the number of fires goes up, firemen show up and reduce the number until it's close to zero again. Separately, if there is a lot of fire, a lot of things might burn down, but then the fire burns itself out. 
2. A very heavy rock. Because it's heavy, it doesn't tend to change.
3. Salt levels in human blood. If it gets too low, human eats more salt. If it gets too high, liver gets rid of it.

1. The even surface of a pond. If I throw in a stone it'll ripple for a while, but the additional activity will dissipate again.
2. The number of tabs I have open in my browser. If it's very few I have no problem opening and keeping new ones. If it's too many, titles become hard to read etc. and I feel reluctant to keep open additional ones and tend to close a bunch of them at once.
3. The amount of social interaction I get. Too little and I feel lonely and reach out to people. Too much and I feel overwhelmed and keep to myself for a while.

1. The dog at the Burrow has a suspiciously regular patrol, during which he looks for food. If you give him food, he will lick your hand and wag his tail gratefully, before returning to the patrol. 
   
   If someone took him away in a car, he would not return to the route.
2. When I move my mouse, my monitor activates. If I do nothing for a while, it will go dark again. 
   
   If I set up a robot which constantly twitched the mouse, the monitor would not go dark, no matter how long I waited.
3. An elastic object, such as a rubber band, will hang such that the force of tension equals the force of gravity. 
   
   If I snap the band, it will not return to its original equilibrium.

• A message with error-correcting codes
• A room heated with a thermostat
• Water in a glass
• Profound distaste for a specific food. Whatever the small perturbation in taste made to it through cooking, you still find it disgusting (for example one of my brothers hate potatoes)
• Most people's political belief, where small perturbations (contradiction, a favorite politician condemned for fraud, a good policy by the outgroup) aren't enough to change the political belief.
• Two system monopoly on election: moving a small number of votes from one or both to other small parties doesn't change the duopoly.

• A message with error-correcting codes: if I want to change the message or see that it is change, it's important to look for the maximal amount of errors that the code can handle, as well as what are the closest message that result from adding just too much error.
• A room heated with a thermostat: If the change is lower than the thermostat's temperature, I must look for some way to cool the room faster than the thermostat can heat it, probably with an exchange with the outside and some sort of heat pump. If the change is higher than the thermostat, then I must look for a source of additional heat that never stops (as the thermostat never makes the room cooler, just wait for it too cool down).
• Water in a glass: some factors are the angle of the glass, its structural integrity, the gravitational force on the water, and whether someone around is thirsty
• Profound distaste for a specific food: factors seem mainly two, either a change of taste due to age (now I like mushroom but I hated them as a kid), or such a transformation of the food that it loses its problematic properties (like my brother can eat thin fries because they barely taste of potatoes)
• Most people's political belief: factors like a change of community, a complete change in the community, so many scandals that the person changed their mind, or someone capitalizing on the discontent while not changing the image of the political belief.
• Two system monopoly on election: factors could be most people agreeing to vote to a third party to break the duopoly, or so few people voting that even small parties have a shot, or siphoning votes for the duopoly into many different parties, splitting everything up.

 Most metrics of productivity/success are at a stable equilibrium in my life. For example: 

1. The work I get done in a day (month?) is fairly constant. If I work hard throughout the day, I eventually feel satisfied and relax for a while. If I relax for too long, I start feeling sluggish and want to get back to working. Sometimes this happens more so on the scale of an entire month (an incredibly productive week followed by a very sluggish week).
2. The amount of socialization I partake in each week is also constant. When I socialize too much my battery is drained and I draw back into myself. If I spend too long cooped up, I reach out to more people.
3. My weight has been pretty constant for the last few years. Every morning I weigh myself. If I my weight is lower than normal I tend to pay less attention to what I'm eating and when my weight is higher than normal I tend to cut back a bit. Even if I eat cake one day, my weight comes back to equilibrium fairly quickly

Shifting equilibrium like these (being more productive, socializing more, getting in better shape, etc.) is obviously desirable. Let's explore that.

In cases like these, direct attempts to immediately change equilibria (like motivating myself to work harder in the moment, going to parties every night for a week, eating an unreasonable calorie deficit to "get fit quick," etc.) is like pushing the ball up the sides of the bowl. Why?

These equilibria are all determined by my own identity. The reason my [productivity/sociability/fitness] is [current level] is because I think of myself as someone who is at that current level of the skill. Making my [current level] jump in the short term does not change my identity and hence does not change my equilibrium.

The only way to "tip the bowl" is to change my identity, how I view myself. Probably the least-likely-to-fail way of doing this is in small increments. For example, instead of instantly trying to be supernaturally productive, first try cutting out YouTube/Twitter/Reddit. When it feels like this is an equilibrium, try reading a paper a week. Then a paper a night. Continue in small steps, focusing on internalizing the identity of being "someone who reads papers" so that the habit of actually reading the papers comes easily.

The number of MHC class I loci. As the number of loci increases, the organism gains an ability to respond to a greater diversity of pathogens and avert evasion of an immune response. At the same time, with each new locus, any T cells that respond to self peptides bound to the new MHC class I molecule must be removed to maintain self tolerance. There is an optimal balance of MHC class I diversity and T cell count. In the case of humans, the optimal number of MHC class I loci appears to be 3.

It is harder than expected not to recycle from known instances. I had to totally avoid physics and markets to feel like finding not remembering examples.

•  There's a lot of somewhat cyclic stochastic processes that I would call a stable equilibrium. My whiteboard tends to have about the same fraction of free space most of the time. Sketching something or deleting something is a fluctuation. Changing my usage habits could make a long term difference.
• The density of social events in my calendar is surprisingly constant. Less is boring, more is exhausting. It regulates itself. Fluctuations include random clusters of important events or little spare time. To constantly change it I could become a recluse or more sociable.
• The mass of the contents of most rooms is dominated by a few long lasting things and is mostly stable. Getting a cup of tea is a small disturbance. Buying new furniture will suddenly change the equilibrium. 

1. A post without any comments on it, may be a stable equilibrium (with regard to total length).

2. Multiple crabs in a bucket.

3. If people pick up trash when there's not a lot of trash, but not if there's a lot, then both 'clean' and 'trash everywhere' can be stable equilibriums.

4. Walking up stairs (or going up an elevator). At a higher level, you maintain your altitude. (And jumping up and down doesn't perturb this into collapse - usually.)

5. A math problem has never been solved. (After being solved, it takes surprisingly little time for new proofs to appear, compared to how long it took the original proof to appear.)

6. Being stuck in Earth's gravity well. Rarely, intense perturbations push things out into space.

Inspired by adamShimi's 'error correcting codes' here:

7. When writing out bibliographies by hand, errors in (copied) citations (proliferating). Or...ambiguity retention. Less ambiguity requires someone who has clarity, but if no one has clarity...

1. The orientation of the shortest road between Chicago and New Orleans. As you progress along the road, you'll notice that it is mostly going south. Sometimes it jitters east or west but generally returns (and fairly quickly) to a southerly orientation. If you blasted a hole in some segment of road, making the shortest road something else, it would return to south-facing pretty quickly. (note: I was trying to think of one that doesn't involve time, at least not fundamentally.)

2. The position of my glass of water on the table. If I push down on it, it becomes ever so slightly lower even though it doesn't feel like it (the table is firm, but on atomic scales the atoms of my glass are getting slightly closer to it!). When I let go, it imperceptably springs back.

3. The number of unread emails in my inbox. It tends to 0 pretty quickly, until there is such a huge surge that I let a few go unread, and then there are X unread emails and that's the new equilibrium for a few months. (I suppose if you went and deleted one of them, then there would be X-1. But on at least one occasion I did this and then as a result slacked off a bit in my email-reading so that I ended up with X again.)

1. For any atom not being part of a living organism is a stable equilibrium.
2. For a spinning top not to spin is a stable equilibrium.
3. Hair length is a stable equilibrium.

1. Deep ocean currents; I expect changes in ocean floor topography and deep-water inertial/thermal changes to matter. I don't expect shallow-water topography to matter, nor wind (unless we have sustained 300+kph winds for weeks straight).
2. Earth's magnetic pole directions; I'm not sure what causes them. I think they're generated by induction from magma movement? In that case, our knobs are those currents. I don't think anything can change the equilibrium without changing the flow patterns, minus stuff like magma composition which can eliminate magnetism.
3. Tourism to, say, Tokyo; the following factors are both compared to other destinations and just Tokyo, and don't span our knob-space. Public opinion and salience, travel costs (time and money), hotel availability, and number of people who speak Japanese. I think that if we know these, most other markets become rounding errors, though I wouldn't be too sure.

1. Planets orbiting the sun: Little disturbances will still result in an elliptic orbit, you need a big disturbance to get the earth fall into the sun or have enough kinetic energy to escape the solar system on a hyperbolic (or in the edge case parabolic) curve.
2. People don't walk naked through streets, because when you try it, you get punished for it. (and other psychology reasons)
3. Your neurons firing in stable similar patterns that make you able to walk upright instead of falling over. Even if you stumble you can often catch yourself because your neurons fire in patterns that are optimized for you standing/walking.

(The factors I can ignore are basically named above.)
Changing the equilibrium:
1. Another star flying through our solar system.
2. Ok "not naked" arguably isn't a that special case out of the possibility space, so it doesn't buy you that much to describe it as equilibrium. There are still many possibilities of how you can be not naked. Still, it is quite non-trivial to get into the "walk naked on the streets" state and you'd probably need an intelligent actor who really wants to achieve that.
3. Being pushed hard. Getting signals from other brain areas that you should sit or lie down.
 

 The distance between a car and its garage. The car tends to be parked at the same place every night, so it returns to 0, despite some perturbations that may happen. However, the car might eventually be moved to a different long-term garage.

 Blood glucose levels. I think this applies to a lot of biological systems, actually. But blood glucose level will "spring back" from local perturbations. 

 Price of a commodity. There can be surges in demand and supply, but generally the price should stay in the same place.

the number of popular X in a human system Y: 

• highly attractive people as a % of the population; because its a competitive force no matter the actual underling state people will just change the thing they are competing on.
  • to change this I imagine you'd have to change "the bowl" ie: add more attention available per human
• Youtube creators as a % of watchtime / engagement

Orbits just came to me, not sure if that counts a novel but I had never thought of them before as a stable equilibrium. They should stay the same unless perturbed by an outside force... but now that I think about it, pushes on an orbit are a permanent change. So I think that changes my answer to a non-stable equilibrium. 

It feels to obvious, but fungible, replicable, commodities equilibrate sales price = MR. 

Political environments should be stable as well until someone changes the system which created them. I'm labelling this as qasi_stable, they find a local minimum based on the rule set, but external forces can eventually break the system (see: all historical empires)