I've got a few home rules I've used for years.

1. Healing Potions: Drinking is a bonus action, using an action player gets the max value. Potion can be thrown 15 ft to a downed target as a bonus action, DC 10 DEX check, brings target to 1 HP. Thrower can choose to spend an action to throw the potion, then they have to pass a DC 12+1 DEX for every 5 ft from target, but if they pass target can roll the healing.

2. Team inspiration: Group shares a pool of inspiration. Up to a max of 5 that can be used at anytime.

3. Inspired saving throws: Players can spend their reaction and a point of inspiration to gain a saving throw re-roll.

4. Initiative Swap: Allow the players to swap initiative rolls with one another before combat starts. Sometimes players have an idea that requires teamwork based on a specific order they’d like to act in, and this allows them to always get the order they want.

Additional smaller rules:

A) Anything you can do.... can be done to you.

B) Roleplay can give modifiers to any roll, or can negate critical hits/success.

C) Every interaction is a chance to roleplay.

D) Once combat begins, diplomacy becomes much harder.

E) When leveling Up, Players can roll or take the average HP, whichever is larger.

F) At Player level 1, Player can take a feat.

G) Caster can spend 2+1 hit dice to recover 1 spell slot up to lvl 3 during a short rest. Can gain additional level for an added hit die per level up to 5th.

@LoamImprovement For 5th edition, I've overwhelmingly played in AL, so ...

But I've seen a LOT of "inspiration can be used for a reroll" and "inspiration can be shared across the table".

I've also seen (too much) "Invisibility == Hidden", which I hate and don't use when I run. I've also seen a large number of variations of the bonus-action-casting rule

AL kinda inherently runs with a "every adventure starts with a long rest" pseudo house rule, which I like.

I use the onednd inspiration gained from nat 1 and only lasting a day.

1d10 or 1d12 for initiative rolls, decided at start of campaign. If you somehow have a +10 init, you should never be in the 50th percentile. Initiative overall is too volatile and random on the d20 range. Tie breaker is Dex score value, followed by Wis>Int>Cha then if it's still a tie roll for it. Ambushes mechanics exist and modify base initiative also; a situational +/-1 because the sun is in their eyes or whatever becomes important and rewards good planning and execution.

Delayed and prepared actions define a logical trigger instead of requiring a reaction. Anything - movement, bonus action, even reactions - can be delayed. Can spend your reaction to either trigger the action early, or cancel it and prevent it from activating. The logic is strict flowchart logic and you are severely limited in how complex it can be/how many triggers can happen based on the action/situation/etc.

Rolled stats are EITHER 3d6*8 choose 6; OR 4d6 drop lowest rolled in a predefined order. You can already break the game 1000 ways with point buy, get good just let people roll. Random stats tend to breed better player creativity anyways. They're so bad they need to be played creatively; or they're so strong the character build gets to be fancy and unique.

I am currently trying the xp to level 3 unconscious rules and its going decently. I had to change it a bit, but it allows players to do actions even at 0 hp for a price. Hard to test since they are over level 12 and they are hard to hurt.

If you drink a healing potion outside of combat its full effect.

Bottled inspirations. They get one in their inventory if they still have one.

Present players play abseetees and get xp as a reward, so I dont redo encounters 10 minutes before the start.

GENERAL CHANGES

1. 10 minutes short rest, 24 hours long rest (only two short rests per long rest). I think it's the sweet spot between the normal rules (which often don't allow enough short rests, severely limiting martials and warlocks) and gritty rules (which I think are a bit too prohibitive), and don't force the players to look for "safe heavens" to rest.

2. Diminutive size for very small creatures. Diminutive creatures, which would include spiders and mosquitoes, only have vision up to 30 feet (they still retain other senses from their stat blocks, if any), and druids gain access to diminutive wildshape at the same level as flying creatures.

3. Also, colossal size for very big creatures, although that's rarely used. Who knows, maybe today's the day you finally fight Allabar, Opener of the way.

4. I like playing Counterspell as a contested check (d20 + spellcasting modifier + level of the spell/counterspell). This way, it's actually two casters wrestling for power, instead of one trying to cast a spell and the other telling them "lol nope", which feels cheap for players.

5. A player can drink a potion with a bonus action. Giving a potion to another player/NPC still requires an action.

6. Something that can be done with a bonus action can also be done with an action - for example, if a wizard uses their bonus action to drink a potion, they can use their action to Misty Step away. "One levelled spell per turn" rule is still in place.

7. Playtest's Exhausted rules in place of the PHB's Exhaustion rules, because they are unusable.

8. No rolled stats. It leads to one party member having all stats above 14 and the other having all stats bar one under 10. With point buy or standard array, everyone begins on equal grounds.

AIMED BUFFS

1. Monk gets additional ki points equal to its PB. It helps making the lower levels feel less like a slog.

2. Arcane Archer has a number of arrows equal to its INT modifier. Small (very much needed) improvement.

3. Berserker doesn't gain exhaustion by using its main subclass feature. Not sure why it was a thing in the first place.

4. All fighters and barbarians get the Martial Adept feat for free with their subclass. As far as I can see, it doesn't break anything and allows for a bit more strategy and diversity.

5. Two-Weapon Fighting (fighting style) allows to make the off-hand attack as part of the attack action if both weapons are light.

6. All sorcerers and warlocks know the spells from their expanded spell list automatically upon reaching the required level (only exception being Wish for Genie warlock). Increases versatility without altering the power level too much.

7. Probably more, I may be forgetting something.

NERFS

1. Silvery Barbs, Pass Without Trace, Polymorph and Wish are banned. In survival campaigns, Purify Food and Drink, Create or Destroy Water, Goodberry and Create Food and Water are banned as well. Banned spells may still be available through purchasable scrolls.

2. Summon/Conjure spells are heavily discouraged, especially those from the PHB that summon a bunch of creatures, as they slow the game down to a crawl and break action economy. I don't ban them because some build are reliant on them (on top of my head, Sheperd Druid and Necromancer Wizard). Find Familiar and familiar-based subclasses such as the Beast Master and the Drakewarden Ranger are allowed, and if players want to summon things, I encourage them to play Tasha's Summon X spells which only summon one big creature in place of eight small ones.

3. Peace Cleric is banned, Twilight Cleric is either nerfed or banned.

I also like to abide by in-character reasons to multiclass, though I haven't had any particular problem players in this regard.

In a similar spirit to your second rule, I like to start off PCs with a free feat since they can be so flavorful for both mechanics and roleplay. I've also given martials a maneuver of their choosing to give martials more to do in combat. I was gratified when the new UA introduced versions of both of these with their feat revisions and things like weapon mastery and rogue's cunning strike.

I've got a few.

1: Massive damage cannot result in instant death. With the exception of fall damage, I can't see a reason that I'd ever want to do this to the players, and even with fall damage, players become unlikely to die from this as soon as they have an average of 35 hitpoints. If I have traps or monsters dealing enough damage to kill instantly, then I've misbalanced my game.

2: Similarly, monsters can't crit, however some monsters will now have new features that allow them to crit, some of which may have expanded crit ranges or inflict a condition on a crit instead, although you can presume a monster can't crit by default.

3: There is no heroic inspiration at all. PCs are already powerful and features like bardic inspiration or the help action already allow PCs to reward eachother.
However I'm interested in an idea which is players just voluntarily taking "momentum tokens" any time they feel like the flow of the session isn't in their favour, this could be from a bad spat of missing or fromcthe DM disallowing a broken combo or anything really. Players can then communally spend the tokens to increment a d6 in the middle of the table (1 token to put it down on the table on 1, 2 tokens to increment it to 2, etc to a max of 6), whenever any creature makes an attack roll or uncontested ability check, they add the value on the die to their roll, however if they're a PC, they add it to all 20 rolls. This means all creatures become more likely to cause their stuff to happen, basically. The big downside is that players can just award themselves tokens at their own volition, which is easily abusable, plus they may get used to a high momentum in a session where they have a +5 or +6 and then feel that the next session has less momentum (the 6d resets by session), and award themselves more tokens. Also if they use the tokens as frustration tokens, it may hurt my feelings. But I like the idea so I continue to workshop it.

4: I use the 2024 rules for exhaustion, unless via the sickening radiance spell.

5: If you are hit by an attack while in death saving throws, you don't automatically fail any, but instead instantly make another death saving throw, still failing on 1-9 but not gaining a success on 10-20. This actually increases tension because I'm more keen to actually hit PCs when down.

Those are the big changes, I do have a few other though,

I don't allow any of the "conjure x" spells, and generally wanna look over any features that add creatures to combat to save time in combat. The summon spells in Tasha's are good, as are most class feature that add creatures to combat, and find familiar.

I don't allow silvery barbs. Not just do I feel it's too strong, I also feel that it's flavourless and entirely interested in altering mechanics that are an abstraction of the storytelling.

I don't allow the lucky feat, however I have a custom feat called borrowed luck, it works the same but if you are reduced to 0 hitpoints, you instantly fail a number of death saves equal to the number of luck points you've spent that long rest.

I have a few bits of race lore such as much fewer races having darkvision but dwarves having access to the light cantrip (and other minor benefits) and a few minor stuff like that, nothing too exciting there.

1. I ban the lucky feat

2. Hexblade is allowed, but only at level 1. And once you have a level in Hexblade, you are forbidden from multiclassing.

3. Any game content that appeared in the SCAG is banned pending my approval.